John 3:22 seems to suggest that he did, saying, “After these things Jesus and his disciples came into the land of Judea, and there he remained with them and baptized.”
Your question is a good one in that it provides us with an opportunity to consider two important lessons:
1. Hermeneutics
Hermeneutics is the science of Bible interpretation and John 3:22 is a prime example of why it is important to acknowledge that all things in scripture are not equally plain.
Some verses are easy to understand, some verses only make sense when interpreted in the light of their broader context, and (as John 3:22 proves) some verses need to be interpreted by other verses which are more clear.
The other verse which is necessary here is John 4:2 which says, “though Jesus himself did not baptize, but his disciples”.
While skeptics call this a contradiction, Bible students receive it as a Spirit-inspired clarification. Jesus did not baptize anyone with his own hand. That much is evident.
Your question also provides us opportunity to consider one more lesson:
2. Sacramentology
Sacramentology is the study of those ordinances which God appointed for his people to observe.
The sacramental lesson of John 3:22 is this:
Though administered by the hands of mere men, the sacraments are still Christ’s sacraments and are to be received as though administered by Christ himself when administered by someone who has been lawfully called and ordained thereunto.
Answered by Pastor Christian McShaffrey