No, there isn’t; but there is evidence that John was a Jew.
- Jesus’ ministry was primarily exclusive to the tribes of Israel (Mat. 15:24). As John and the other disciples were people Jesus came to minister to, John would have been a Jew.
- Jesus probably selected the twelve disciples to represent Israel in some way (cf. Gen. 49:28; Ex. 24:4; Num. 1:44; Deut. 1:23; Josh. 3:12; Ezra 6:17; Ezek. 48:31; 1QM 2:2-3; 1QM 5:2-3; Pesiq. Rab. 4),1 which would also indicate that John was an Israelite, a Jew.
- Jesus shared his mission (directed towards the Jews) with his twelve disciples (Mat. 10:5-6), indicating that they (including John), involved in Jesus’ Jewish ministry to Jewish people, were Jews.
- It’s possible that John was Jesus’ cousin,2 also an indication of his Jewishness.
A reconstruction of the face of a typical first century Galilean Jew has been made using forensic science and may give some indication of what John might have looked like.
1. Dale C. Allison, Constructing Jesus (London: SPCK, 2010), p. 71 n. 172. Also see Scot McKnight, ‘Jesus and the Twelve’ (12/05/04) on bible.org (accessed 06/08/15)
2. ‘That John’s mother’s name was Salome is an inference from Mk. 16:1 and Mt. 27:56…Salome is usually regarded as the sister of Mary the mother of Jesus, because [of] Jn. 19:25…If this identification is correct, John was a cousin of Jesus on his mother’s side.’ (R. V. G. Tasker, ‘John, The Apostle’ in New Bible Dictionary 2nd edn [Leicester: IVP, 1962], p. 601)