"The Pope, Bishop of Rome and Peter's successor, "is the perpetual and visible source and foundation of the unity both of the bishops and of the whole company of the faithful." "For the Roman Pontiff, by reason of his office as Vicar of Christ, and as pastor of the entire Church has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered." (CCC # 882)
There is no scriptural basis for saying that the pope is the Vicar of Christ. Jesus is our Savior and our Mediator. Jesus Christ is our blameless High Priest. He is therefore superior to the Old Testament priesthood. He set forth an everlasting covenant of grace for all those who place their trust in Him. Christ is our substitute and representative before God. There exists no earthly representative who can carry on any of the tasks that He has taken upon Himself.
Moreover, Jesus Christ Himself promised that the Holy Spirit would be present on earth during His physical absence. The Holy Spirit makes known the things of God (John 14:26; 1 Corinthians 2:12). The Holy Spirit guides believers (John 16:13). The Holy Spirit comforts believers (John 14:16-18). The pope has taken on titles and roles that Scripture reserves for no mere man. This historical information from the Encyclopedia Britannica is relevant here:
"In the Roman Empire as reorganized by Emperor Diocletian (reigned 284–305), the vicarius was an important official, and the title remained in use for secular officials in the Middle Ages. In the Roman Catholic Church, “vicar of Christ” became the special designation of the popes starting in the 8th century, and eventually it replaced the older title of “vicar of St. Peter.”
The title "Vicar of Christ" is simply one of many unbiblical titles that the pope has used to extol himself.