Acts 18:18 tells us:
Paul stayed on in Corinth for some time. Then he left the brothers and sistersa and sailed for Syria, accompanied by Priscilla and Aquila. Before he sailed, he had his hair cut off at Cenchreaed because of a vow he had taken.
So he cut his hair because of a vow. What kind of vow? The Bible doesn’t say, but we can reasonably presume it was a vow to God. Paul also refers to a vow that his travel companions made in Acts 21:23 and it is in context of their koshersness, so to speak.
So what is the vow and why did Paul make it? We don’t know, the Bible doesn’t say and so any thought is conjecture. Based on conjecture then:
— perhaps a Nazarite Vow which involves growing your hair out
— More likely a personal spiritual vow akin to fasting.
— And course, Acts 18 may simply be the first ever reference to “No Shave November!”
But jokes aside, it appears that the vow had a jewish root and partially showed jewish people of Paul’s orthodoxy, opening them up to his conversation about Jesus as Messiah.