Yes, and Paul taught the same as James said that faith without works is dead.
Your faith will lead you to do the spiritual works commanded by the Lord Jesus, if those spiritual works are not performed in ones life they have a dead faith which does not lead to salvation. People want so hard to make works an ugly thing, but the bible says that those that are done for self or to earn are bad. Those that are done out of the love for Him are spiritual works done for spiritual growth and a part of a believers life. Lord Jesus constantly says those who believe in Him will show it in their actions, and those who don't their actions will show that to.
Then He also gives warnings so that if somebody tells us we only have to believe, but don't need to have works that show it then you are being falsely taught. Like telling people if you deny to help others, you deny Him. And those who tell people they don't have to forgive others, for He says we do, and if we don't we will not be forgiven of ours.
Then He also tells us exactly what it means to believe in Him, He says it is those who come and hear and then do what He said.
By all this we can see that a saving faith, will have repentance, confession, and yes baptism as a part of it. For they were all taught and commanded by the Lord, and we are told by Him if you love Him you will obey and keep these teachings/commands.
Finally water was part of the cleansing of the OT covenants, water was part of the baptism during John the baptist and Jesus earthly ministry, water was still part of baptism during the Acts of the apostles ( their ministry ). Peter, and Paul which are the main two used and did water in baptism.
Acts 19:3-6
3 And he said, “Into what then were you baptized?” They said, “Into John's baptism.” 4 And Paul said, “John baptized with the baptism of repentance, telling the people to believe in the one who was to come after him, that is, Jesus.” 5 On hearing this, they were baptized in[a] the name of the Lord Jesus.6 And when Paul had laid his hands on them, the Holy Spirit came on them, andthey began speaking in tongues and prophesying..
Paul says here that John's baptism in water was for the remission of sins, and the baptism in water that is done now is in the name of Jesus. Notice how after they were baptized, then Paul laid hands on them and they received the Holy Spirit.