I thought that he was born in modern day Turkey and was a Roman citizen. That’s all I know. In what sense was he a Jew or when did he become one?
The fact that he lived in Tarsus and was a Roman citizen do not detract from the fact that he was a Jew. There was already a Diaspora at that point.
[Acts 22:2-3] (And when they heard that he spake in the Hebrew tongue to them, they kept the more silence: and he saith,) I am verily a man which am a Jew, born in Tarsus, a city in Cilicia, yet brought up in this city at the feet of Gamaliel, and taught according to the perfect manner of the law of the fathers, and was zealous toward God, as ye all are this day.