In the book of Acts baptism is an initiatory rite closely associated with conversion to Christianity.
The following examples make it clear that believing, repenting and being baptised go together in the book of Acts.
Acts 2:38 Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit.
Acts 8:12-13 But when they believed Philip as he proclaimed the good news of the kingdom of God and the name of Jesus Christ, they were baptized, both men and women. Simon himself believed and was baptized. And he followed Philip everywhere, astonished by the great signs and miracles he saw.
Acts 10:43-48 All the prophets testify about him that everyone who believes in him receives forgiveness of sins through his name. While Peter was still speaking these words, the Holy Spirit came on all who heard the message. The circumcised believers who had come with Peter were astonished that the gift of the Holy Spirit had been poured out even on Gentiles. For they heard them speaking in tongues and praising God. Then Peter said, “Surely no one can stand in the way of their being baptized with water. They have received the Holy Spirit just as we have.” So he ordered that they be baptized in the name of Jesus Christ. Then they asked Peter to stay with them for a few days.
I could put Acts 8:35-39, 16:31-34, 18:8, 19:4-5 into the mix because they all show a strong connection between faith and Baptism but you can look them up in your own time. These passages all show a very strong connection between faith and baptism. It is like Acts is saying that if you want to be baptised you have to be a believer. Isn’t this evidence enough to say that only believers baptism is a legitimate baptism?
No I hear many of you say because of Acts 10 where Cornelius’s whole household is baptised (10:46). The argument here and in the baptisms of other households (i.e. Lydia in Acts 16 and Crispus in Acts 18) is that they baptised the whole household therefore the person who baptised them would have baptised any infants in the household. Two things could be said about this point. Firstly, Luke is frustrating in the scant amount of detail he clothes these narratives with. Cornelius might have been a young man with a young family or an old man with no children at home. He and his wife could have been barren, we just do not know. So in response to the scant detail we must not press the text into saying something it is not. We are left saying that he baptised the whole household and we do not know who comprised that household. Therefore, to use this text as a proof text for infant baptism is pressing the text further than it can be pressed. Secondly, we need to see that the people who were baptised in 10:48 are described as hearing the word (10:44) and speaking in tongues (10:48) these are signs of belief in the books of Acts. Therefore, it is exegetically safe to say that Cornelius’s household was baptised because they believed not because the early church baptised infants. Therefore even though Acts 10 is used by proponents of infant baptism it is actually a text, when exegeted closely, that comes out in favour of believers baptism.
In conclusion, the book of Acts links baptism with belief and repentance. Therefore those who must be baptised must be able to have faith in the lordship and saving work of Jesus.