‘Compatibilism’, according to D.A. Carson, involves the acceptance that both the following propositions are taught in Scripture:-

1. God is absolutely sovereign, but his sovereignty never functions in Scripture to reduce human responsibility.
2. Human beings are responsible creatures—that is, they choose, they believe, they disobey, they respond, and there is moral significance in their choices; but human responsibility never functions in Scripture to diminish God’s sovereignty or to make God absolutely contingent.

The temptation to emphasise one of these at the expense of the other is great, but must be resisted if we are to remain faithful to the Bible’s witness.

Among the many Bible passages that demonstrate divine sovereignty and human responsibility, Carson cites: Genesis 50:19-20; Leviticus 20:7-8; 1 Kings 11:11-13, 29-39; 12:1-15 (cf. 2 Kings 10:15; 11:4) 2 Samuel 24; Isaiah 10:5-19; John 6:37-40; Philippians 2:12-13; Acts 18:9-10; and Acts 4:23-30.  To this list should also be added Acts 2:23.

In connection with Acts 4:23-30, Carson comments that all Christians become compatibilists when they think about the cross:

‘There is no alternative, except to deny the faith. And if we are prepared to be compatibilists when we think about the cross—that is, to accept both of the propositions I set out at the head of this chapter as true, as they are applied to the cross—it is only a very small step to understanding that compatibilism is taught or presupposed everywhere in the Bible.’

We are all compatibilists at the cross.

See this by Justin Taylor