How are your sins washed away, by calling on the name of Jesus? Baptism identifies with this truth.
The words of Ananias to then Saul of Tarsus in Acts 22:16 contains much of the language in the question: "And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on his name." While baptism and calling on the name of the Lord were the only instructions that Ananias gave Saul, the context makes clear that Saul's baptism was preceded by both faith and repentance. It was faith that led him to obey the Lord's command to go into Damascus and await the Lord's appointed messenger. It was repentance that led him to three days of prayer and fasting. Many scholars equate "calling on his name" with the good confession. (See Classes: The Church: Lesson 5, especially page 10. It would also be good to review Classes: Questions: Lesson 3, Baptism.) Clearly baptism and calling of the name of the lord are necessary parts of having sins washed away. Thus, the answer is "yes." Baptism does identify in a very specific way with washing away sins. Paul is absolute proof that one who has not be baptized for the remission of sins has not had his sins washed away or forgiven. To speak of Saul's forgiveness on the road to Damascus is to contrary to scripture. God's appointed spokesperson clearly told Saul in Damascus that his sins had not yet been forgiven. It would have been impossible to remove that from which he had already been cleansed!
You Must Hear the Gospel
Romans 10:17
You must hear the gospel and then understand and recognize that you are lost without Jesus Christ no matter who you are and no matter what your background is. The Bible tells us that “all have sinned, and come short of the glory of God.” (Romans 3:23) Before you can be saved, you must understand that you are lost and that the only way to be saved is by obedience to the gospel of Jesus Christ. (2 Thessalonians 1:8) Jesus said, “I am the way, the truth, and the life: no man cometh unto the Father, but by me.” (John 14:6) “Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.” (Acts 4:12) "So then faith cometh by hearing, and hearing by the word of God." (Romans 10:17)
You Must Believe
Hebrews 11:6
You must believe and have faith in God because “without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11:6) But neither belief alone nor faith alone is sufficient to save. (James 2:19; James 2:24; Matthew 7:21)
You Must Repent
Acts 3:19
You must repent of your sins. (Acts 3:19) But repentance alone is not enough. The so-called “Sinner’s Prayer” that you hear so much about today from denominational preachers does not appear anywhere in the Bible. Indeed, nowhere in the Bible was anyone ever told to pray the “Sinner’s Prayer” to be saved. By contrast, there are numerous examples showing that prayer alone does not save. Saul, for example, prayed following his meeting with Jesus on the road to Damascus (Acts 9:11), but Saul was still in his sins when Ananias met him three days later (Acts 22:16). Cornelius prayed to God always, and yet there was something else he needed to do to be saved (Acts 10:2, 6, 33, 48). If prayer alone did not save Saul or Cornelius, prayer alone will not save you. You must obey the gospel. (2 Thess. 1:8)
You Must Confess
Romans 10:9
You must confess that Jesus Christ is the Son of God. (Romans 10:9-10) Note that you do NOT need to make Jesus “Lord of your life.” Why? Because Jesus is already Lord of your life whether or not you have obeyed his gospel. Indeed, we obey him, not to make him Lord, but because he already is Lord. (Acts 2:36) Also, no one in the Bible was ever told to just “accept Jesus as your personal savior.” We must confess that Jesus is the Son of God, but, as with faith and repentance, confession alone does not save. (Matthew 7:21)
You Must Be Baptized
Acts 2:38
Having believed, repented, and confessed that Jesus is the Son of God, you must be baptized for the remission of your sins. (Acts 2:38) It is at this point (and not before) that your sins are forgiven. (Acts 22:16) It is impossible to proclaim the gospel of Jesus Christ without teaching the absolute necessity of baptism for salvation. (Acts 8:35-36; Romans 6:3-4; 1 Peter 3:21) Anyone who responds to the question in Acts 2:37 with an answer that contradicts Acts 2:38 is NOT proclaiming the gospel of Jesus Christ!
You Must Be Faithful Unto Death
Revelation 2:10
Once you are saved, God adds you to his church and writes your name in the Book of Life. (Acts 2:47; Philippians 4:3) To continue in God’s grace, you must continue to serve God faithfully until death. Unless they remain faithful, those who are in God’s grace will fall from grace, and those whose names are in the Book of Life will have their names blotted out of that book. (Revelation 2:10; Revelation 3:5; Galatians 5:4)