I think he was a Jew.

..there isn't a lot of evidence of Pilate's personal history, but..from what I read, it doesn't appear he would have been a Jewish person. As you probably noted in the Bible record, he was the provincial governor of Judah during Jesus's earthly ministry. (Luke 3:1) When the Jewish leaders came to Pilate to lodge charges against Jesus for being subversive,they would not enter his premises as he was a Gentile.