In ancient Judaism there were certain customs, rituals, and ceremonies involving the removal of one’s hair,3 perhaps most notably the Nazarite vow (Num. 6:1-21). However, Paul’s haircut at Cenchrea was unlikely connected to the Nazarite vow, which would have required the burning of the hair in the presence of a priest in the Jerusalem temple. In ancient Judaism there were any number of personal vows or solemn pledges to God any Jewish person could make, which were entirely voluntary albeit regulated (Deut. 23:21-23).
Even though Paul, as a Christian, was free from the Law of Moses, he was still an ethnic Jew and maintained certain aspects of his cultural heritage (Acts 16:3; 21:20-24; 22:17; 28:17; 1 Cor. 9:20). Moreover, the transition from old covenant Judaism to Christ’s new covenant system was not instantaneous but involved the gradual unfolding of divine revelation until the New Testament was completed. Paul, as a Jewish Christian, lived during this transitional period. His vow and haircut at Cenchrea, perhaps in response to the Lord’s providential protection in Corinth, were indicative of his background and ethnic heritage rather than his Christian faith.
--Kevin L. Moore
1 Acts 18:6, 9-10, 12-17; 1 Cor. 2:3; 2 Cor. 1:5-6, 19; 1 Thess. 3:7; 2 Thess. 3:2.
2 Note the distinction in 1 Corinthians 11:6. The verbal keírō conveys the sense of “shear” or “cut short” (Acts 8:32; 18:18; 1 Cor. 11:6), while zuráō means to completely “shave” (Acts 21:24; 1 Cor. 11:5-6); compare Ezek. 44:20. Because of the somewhat awkward and ambiguous word order in the Greek text of Acts 18:18, a number of commentators claim that it was Aquila who had taken the vow and had his hair removed.
3 Lev. 13:33; 14:8-9; Num. 8:7; Deut. 21:12; Jer. 7:29; Ezek. 5:1; 44:20; Mic. 1:16; Acts 21:24.
Image credit: adapted from https://www.lcgeducation.org/the-nazarite-vow/