This is a double-edged question, and one for which one may find two sorts of answers:
- According to accepted church practice, can a Baptist deacon baptize?
- According to the Bible, can a Baptist deacon baptize?
Second, according to the Bible, can a Baptist deacon baptize? This removes the discussion from what is practiced to the underlying rule of our practice, the word of God. Still, some Baptist churches interpret the "rule" differently and still may answer either "yes" or "no". While this can be a multi-pronged investigation of biblical principle and New Testament practice, for many the decision will be made on the interpretation of Acts 8:12-38. While "the commission" of Matthew 28:18-20 is spoken directly to the apostles, we find in the book of Acts at least two people not among the apostles who baptize -- Philip (Acts 8) and Ananias (Acts 9:5,9,18). The Philip who baptizes in Acts chapter 8 is the same Philip of Acts 6:5. This Philip is one of the seven, the first collection of deacons set apart in the church of Jerusalem. If this deacon baptized in New Testament times, there should be little question for us now -- according to the Bible a Baptist deacon can baptize.
 Many of these might say something like, "Although normally the pastor of a church baptizes and presides at the Lord’s Supper, any member designated by the church could do so."
 This is not Philip the apostle, but the Philip who is mentioned in Acts 6:5. No other disciples named Philip are mentioned in Luke's history of the Acts. Note: (1) the apostles were not scattered but continued at Jerusalem (Acts 8:1), while Philip was among the dispersion (Acts8:4-5); (2) the apostles are distinguished from Philip (Acts 8:14,18,25); (3) the apostles, but not this Philip, had the power of communicating the Spirit by laying on of hands (Acts 8:14-18); (4) the apostles returned to Jerusalem, but Philip was called to go the way toward Gaza (Acts8:25-26); and (5) Philip passed through many cities preaching until he came to Caesarea, the place where Philip the evangelist is found in Acts 21:8. (A deacon who was preaching would more appropriately be called an evangelist, while an apostle would have been identified as an apostle.)
 These were not called deacons in Acts 6, but they performed some of the same duties mentioned in that church office (1 Tim. 3:8-13).The deacons were charged with oversee the distribution of monies and provisions to the needy among the congregation. The word deacon/diakonoi means "servant", and these men were certainly servants of the church. Someone has noticed, "They could claim the same promise for faithful service that Paul specifically made to deacons in 1 Timothy 3:13." Though Luke never calls them the noun diakonoi, the verb diakoneo is "serve" in verse 2. There are two offices in the New Testament -- elders and deacons -- and the calling, setting apart and service of Acts 6 agrees well with the calling, setting apart and service of deacons. One of the early post-apostolic church father, Irenaeus,writing around AD 180, calls Stephen (one of the seven in Acts 6) a deacon (Against Heresies 3.12.10).