ANSWER: There is nothing in the Bible that states who can and cannot perform the ceremony known as baptism.
Let us take a brief look at the most well-known mass baptism in the New Testament - the one which occurred on the day of Pentecost. If we take a close enough look we will find that it would have been nearly IMPOSSIBLE for a group of eleven men (the apostles) to have taken care of the baptismal needs God generated that day!
Consider the following. On Pentecost Peter started speaking at about 9:00 AM (Acts 2:15). When he finished, God caused about three thousand people to repent of their sins, accept Jesus as their Savior, and request to be baptized (Acts 2:41). If we assume Peter's sermon took about an hour, that would leave only about eight hours (480 minutes) left of daylight. Let us also assume that only the twelve apostles did all the baptisms and 'laying on hands' on the believer in order to pray God gives him his Spirit. This would mean each apostle, of necessity, would have to baptize 250 people (3000 / 12). They would only have less than TWO MINUTES to do what is required for each repentant believer IF they worked non-stop for eight continuous hours without any breaks! In short, it would be nearly impossible for twelve people to do all the work.
Consider, however, if all the one hundred and twenty disciples (Acts 1:15) present on Pentecost and who received God's spirit participated in baptizing new believers. Each one would have to baptize about 25 people in eight hours - a far more realistic approach. In this scenario, the person doing the baptizing could use up to fifteen minutes of their time on each person and STILL have plenty of time for breaks and to eat.
Each baptism would, according to scripture, be done "in the name of Jesus" (Acts 4:8 - 12, Colossians 3:17).
The Bible does NOT state nor teach that a person who has a particular title, rank or status in the church MUST perform a baptism or lay hands on the new believers in order for them to receive God's spirit. God commanded Ananias, who was not referred to as minister, evangelist, church elder, apostle, etc., to baptize Paul (Acts 9:10 – 18).
There is no Biblical instruction as to who can baptize - in spite of what some "ordained" ministers may say!