1 When therefore the Pharisees had heard that Jesus made and baptized more disciples than John,
2 They sought more diligently some means that they might put him to death; for many received John as a prophet, but they believed not on Jesus.
3 Now the Lord knew this, though he himself baptized not so many as his disciples; (New Testament | John 4:1—3 [RLDS Inspired Version, 1867])
On pp. 115-16 of his book, How Did Christianity Really Begin? A Historical-Archaeological Approach (Evanston, Ill.: Religion and Ethics Institute, 1992), Howard W. Teeple discusses some of the evidences supporting the claim Jesus Himself, and not just his disciples, baptised people. While I disagree with the liberal bent throughout the volume (e.g., a priori rejection of predictive prophecy and a full-blown acceptance of metaphysical naturalism), the points he makes are worthy of consideration on this particular issue:
1. Since Jesus continued John’s message after John was arrested, he would probably continue the baptism as well as the message, for the two features were closely related.
2. A passage in the Gospel of Signs, incorporated in John 3:22, states that Jesus baptized in Judea.
3. John 4:1 states that Jesus baptized more disciples than John. (The next verse states that Jesus himself did not baptize, but his disciples did. This verse, however, is an insertion by a later scribe [as linguistic evidence shows], who was probably influenced by the synoptic gospels.)
4. According to Acts 2:38 Peter preached, “Repent and be baptized . . .” The apostles baptized, and the more plausible explanation is that they were continuing Jesus’ practice. If they were not, why did they introduce the ritual? Apparently Jesus continued John’s practice after John’s death, and the disciples continued Jesus’ practice after his death. Strong evidence is the fact that John, Jesus, and the disciples all combined repentance and baptism, a distinctive feature.
5. The absence in the synoptic gospels of any tradition that Jesus baptized others does not prove that he did not do so . . . The authors may have omitted it in an effort to separate the careers of the two men. The Gospel of John deals with the problem by saying Jesus baptized more disciples than John. The synoptics’ solutions are to omit any mention of Jesus’ baptizing and to claim that he—unlike John—baptized with the Holy Spirit . . .
In the light of the total evidence, it is very probable that Jesus did baptize.