Yes. The Bible treats the Holy Spirit as fully God: He is called God directly, shares the divine name, and possesses divine attributes and works. He is a distinct Person, but the same divine essence as the Father and the Son.
Not a summary of these passages: the passages themselves. Read them, then come back to the study below.
The study
What the Scripture says
1
Scripture calls Him God directly
When Ananias lied about the price of the land, Peter said: 'Why has Satan filled your heart to lie to the Holy Spirit… You haven't lied to men, but to God.' The equation is explicit and unmistakable: to deceive the Holy Spirit is to deceive God.
But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit, and to keep back part of the price of the land? While you kept it, didn’t it remain your own? After it was sold, wasn’t it in your power? How is it that you have conceived this thing in your heart? You haven’t lied to men, but to God.”But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God.
Jesus commanded baptism 'in the name of the Father and of the Son and of the Holy Spirit': a single name shared by all three. Paul's benediction likewise places the grace of Christ, the love of God, and the fellowship of the Spirit side by side as the one source of every blessing.
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
The grace of the Lord Jesus Christ, the love of God, and the fellowship of the Holy Spirit, be with you all. Amen.The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost, be with you all. Amen. The second epistle to the Corinthians was written from Philippi, a city of Macedonia, by Titus and Lucas.
The Spirit is called 'the eternal Spirit'; the psalmist asks 'Where could I go from your Spirit?' He is everywhere; and Paul says the Spirit searches all things, even the deep things of God, knowing the mind of God as only God can.
how much more will the blood of Christ, who through the eternal Spirit offered himself without defect to God, cleanse your conscience from dead works to serve the living God?How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
Where could I go from your Spirit? Or where could I flee from your presence? If I ascend up into heaven, you are there. If I make my bed in Sheol, behold, you are there! If I take the wings of the dawn, and settle in the uttermost parts of the sea; Even there your hand will lead me, and your right hand will hold me.Whither shall I go from thy spirit? or whither shall I flee from thy presence? If I ascend up into heaven, thou art there: if I make my bed in hell, behold, thou art there. If I take the wings of the morning, and dwell in the uttermost parts of the sea; Even there shall thy hand lead me, and thy right hand shall hold me.
But to us, God revealed them through the Spirit. For the Spirit searches all things, yes, the deep things of God. For who among men knows the things of a man, except the spirit of the man, which is in him? Even so, no one knows the things of God, except God’s Spirit.But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God. For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
The Spirit hovered over creation, He gives new birth, and He will raise our mortal bodies. Regeneration, being born again, is His work, and the resurrection itself is attributed to Him. These are works only God can do.
The earth was formless and empty. Darkness was on the surface of the deep and God’s Spirit was hovering over the surface of the waters.And the earth was without form and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
Jesus answered, “Most certainly I tell you, unless one is born of water and spirit, he can’t enter into the Kingdom of God! That which is born of the flesh is flesh. That which is born of the Spirit is spirit. Don’t marvel that I said to you, ‘You must be born anew.’ The windblows where it wants to, and you hear its sound, but don’t know where it comes from and where it is going. So is everyone who is born of the Spirit.”Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God. That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. Marvel not that I said unto thee, Ye must be born again. The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth: so is every one that is born of the Spirit.
But if the Spirit of him who raised up Jesus from the dead dwells in you, he who raised up Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you.But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you.
Being God does not mean being the Father or the Son. The Spirit is sent by the Father at the Son's request; He proceeds from the Father and testifies about the Son. He is a Person in eternal relationship, not a mode or a mask.
I will pray to the Father, and he will give you another Counselor, that he may be with you forever,— the Spirit of truth, whom the world can’t receive; for it doesn’t see him, neither knows him. You know him, for he lives with you, and will be in you.And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
“When the Counselorhas come, whom I will send to you from the Father, the Spirit of truth, who proceeds from the Father, he will testify about me.But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit, and to keep back part of the price of the land? While you kept it, didn’t it remain your own? After it was sold, wasn’t it in your power? How is it that you have conceived this thing in your heart? You haven’t lied to men, but to God.”But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God.
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
But to us, God revealed them through the Spirit. For the Spirit searches all things, yes, the deep things of God. For who among men knows the things of a man, except the spirit of the man, which is in him? Even so, no one knows the things of God, except God’s Spirit.But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God. For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
how much more will the blood of Christ, who through the eternal Spirit offered himself without defect to God, cleanse your conscience from dead works to serve the living God?How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?