The "Sinner's Prayer" is a corrupt method of evangelism invented in the 20th century. Romans 10:9-14 teaches justification by grace alone through repentant faith alone in Jesus Christ alone. The lost do not need to repeat a prayer, ask Jesus into their hearts, or confess anything with their mouths in order to be justified before God. Confession with the mouth and calling upon the Lord are results of justification and evidences that the one who manifests these fruits of the new birth as marks characterizing his life has been born again. One must first believe with one's heart and receive Christ's righteousness (Romans 10:10) before he can confess Christ in the sense the Apostle Paul meant it in Romans 10:9. Calling on the Lord is part of the Christian's life of prayer, not a formula for a lost person to become saved.
Furthermore, Revelation 3:20 does not speak about asking Jesus into one's heart. The verse is about the Lord Jesus Christ outside the "door" of the church at Laodicea and seeking to come in to fellowship with them, not about a lost person praying to ask Christ to penetrate into his heart.
As Dr. Paul Chitwood demonstrated in his Ph. D. dissertation on the sinners prayer, "The Sinner's Prayer: A Historical and Theological Analysis," the corruption of Biblical soulwinning involved in "sinner's prayer" evangelism did not exist for the overwhelming majority of church history. Never in the Old Testament or the New Testament is the sinner's prayer a way of salvation. Neither the Lord Jesus Christ, nor the Apostles, ever employed it. Baptist and evangelical preaching and counseling of awakened and seeking sinners made no mention of a "sinner's prayer" as a method of regeneration until the 20th century. Soulwinners such as Charles Spurgeon did not counsel the lost to repeat a prayer. The method was popularized among Baptists by people such as Jack Hyles and Carl Hatch who replaced soulwinning with salesmanship.
What is more, assurance of salvation does not come by remembering one has prayed the sinner's prayer, nor should people who doubt salvation be told to repeat a sinner's prayer, contrary to the advice of Curtis Hudson and the Sword of the Lord. The lost must be directed to look directly to the Lord Jesus Christ, His perfect sacrifice for sin, and resurrection from the dead for salvation rather than being told to say a prayer. While it is appropriate for a lost sinner to be crying to God for mercy (Luke 18:13), whether he prays or not does not determine if he will be born again, but whether, enabled by the grace of the Holy Spirit, he turns from his sins in repentance and trusts, by grace alone, in Christ alone in saving faith. The lost must be justified by repentant faith alone, not by faith plus the repetition of a sinners prayer.
The study "An Exegesis and Application of Romans 10:9-14 for Soulwinning Churches and Christians in Relation to the Question of the “Sinner’s Prayer” here:
https://faithsaves.net/romans-10-sinners-prayer/
provides more detail on this topic.
See also:"Will I Be Saved if I Ask Jesus to Come into my Heart or Repeat the Sinners Prayer?"
https://faithsaves.net/sinners-prayer/
"The Other Jesus: The Gospel Perverted By Asking Jesus into Your Heart"
https://faithsaves.net/asking-jesus-into-your-heart/
"The Sinners Prayer: A Historical and Theological Analysis," by Paul Harrison Chitwood
https://faithsaves.net/the-sinners-prayer/
as well as:
"How to Proclaim the Gospel: A Guide to Personal Soulwinning--Notes and a Sample Method for Evangelistic Preaching and Personal Work"
https://faithsaves.net/soulwinning/
"Evangelism Video: How to Proclaim the Gospel and do Biblical Soulwinning"
https://faithsaves.net/evangelism-video/
"Soteriology: The Doctrine of Salvation"
https://faithsaves.net/soteriology/
Evangelistic Bible studies:
https://faithsaves.net/Bible-studies/