Believing could definitely be called a work, but a work of the Holy Spirit. But let me provide biblical proof text so that any argument against this can be an argument against God.
- First, belief is the work of the Holy Spirit:
10 He was in the world, and the world was made through Him, and the world did not know Him. 11 He came to His own, and His own did not receive Him. 12 But as many as received Him, to them He gave the right to become children of God, to those who believe in His name: 13 who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. John 1:10-13
Let's parse this passage. In context, "He" in verse 10 refers to the "word made flesh", who we understand to be Jesus the Christ. Verse 10 tells us that the world didn't know Him. Jesus later tells His disciples that they are not of the world.
19 If you were of the world, the world would love its own. Yet because you are not of the world, but I chose you out of the world, therefore the world hates you. John 15:19
To be clear, the disciples did not choose Jesus, He chose them, God incarnate elected to make His disciples different from the world and not of the world. If choice is a work, it was Jesus' work, it was God incarnate's work.
Going back to chapter 1 of John's gospel, we can see that only those called out of the world could "know" the Lord.
Verse 11 continues to say that "He" was not received by His own. Since His disciples, the called out ones, did receive Him, this verse would only apply to His family, His nation, or both.
The Lord grew a large following, but He taught them in parables, only teaching His disciples, His called out ones, the meaning of those parables. So far, everything in the passage is Jesus' work, God incarnate's work.
Verses 12 and 13 go on to express a single idea. Though they've been separated by a colon in our translation, the colon is a modern addition to break up this very long "run on" sentence. Below I've removed the added punctuation in order to display the original translation:
"But as many as received Him, to them He gave the right to become children of God, to those who believe in His name who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God."
So the text plainly says that those that received Him (His called out ones, His disciples) were given "the right to become children of God", (His gift, His work.)
The sentence goes on to say that receiving Him is believing Him, and that those who believe in His name (Jesus, translated as Yah havah our savior) were born by the will of God, not by man's will or the will of the flesh. Again this describes God's work, not ours.
I understand that chapter 1 of John's gospel is frequently misunderstood or misinterpreted, but it says things very plainly that the carnal mind just rejects outright.
We believe that we are making a choice to believe the Lord, but the passage is teaching that God chose to give us a new birth according to His will and that the consequence of that new birth is our belief in the Lord Jesus Christ.
Our salvation, our faith is entirely His work and not our own.
We can resist His work and grieve His Spirit, but being born again of His Spirit makes us His spiritual children and subject to His discipline.
He guides us into His righteousness the easy way through obedience, the hard way through correcting discipline when we are disobedient, but it is entirely His work.
Consequently the Apostle Paul teaches us this principle with the exhortation:
12 Therefore, my beloved, as you have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling; 13 for it is God who works in you both to will and to do for His good pleasure. Philippians 2:12-13
This isn't a particularly difficult doctrine to comprehend and is taught plainly in the text of scripture, but it's a difficult doctrine to apprehend as it seems to disagree with the perception of our experience. Scripture tells us that God is working in us, but we can't see Him working, so we naturally assume that we are "working" or believing God by our own efforts, rather than the spiritual reality that He is creating us anew by His efforts.
And we know that all things work together for good to those who love God, to those who are the called according to His purpose. Romans 8:28
Who works all things together for good?
It certainly isn't us, but a Sovereign God who is in control over all things, so again our experience, our knowledge, our relationships, our faith, are all the result of His work and not our own. All glory belongs to Him and He does not share His glory with another. Amen.