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.”
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,
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?
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.
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.
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.
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.”
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.
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.
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 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.
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?