Vicar of Christ

882 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."
936 The Lord made St. Peter the visible foundation of his Church. He entrusted the keys of the Church to him. the bishop of the Church of Rome, successor to St. Peter, is "head of the college of bishops, the Vicar of Christ and Pastor of the universal Church on earth"
Catechism of the Catholic Church, Part 1, Section 2, Chapter 3, Article 9, Paragraph 4

A definition of the word "vicar" from this website:
QUOTE
The word vicar comes from the Latin word vicarius meaning substitution. The on-line version of the Pocket Catholic Dictionary by John A. Hardon, S.J. defines the Vicar of Christ as, "The Pope, visible head of the Church on earth, acting for and in the place of Christ. He possesses supreme ecclesiastical authority in the Catholic Church..."
UNQUOTE

Is there an office called "Vicar of Christ" described in the Bible?

Christ is the Head of the Church
And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence. (Colossians 1:18 KJV)
For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body. (Ephesians 5:23 KJV)

Christ is the Cornerstone of the Church
For other foundation can no man lay than that is laid, which is Jesus Christ. (1 Corinthians 3:11 KJV)

Christ is the Foundation of the Church

So then you are no longer foreigners and strangers, but fellow citizens with the saints, and members of God’s household, built on the foundation of the apostles and prophets, with Christ Jesus Himself as the cornerstone. The whole building, being put together by Him, grows into a holy sanctuary in the Lord. You also are being built together for God’s dwelling in the Spirit. (Ephesians 2:19-22 HCSB)

Christ is the Builder of the Church
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. (Matthew 16:18 KJV)

When Jesus is no longer on earth physically, God will sent the Holy Spirit. No vicar is needed.
And I will ask the Father, and He will give you another Counselor to be with you forever. He is the Spirit of truth. The world is unable to receive Him because it doesn't see Him or know Him. But you do know Him, because He remains with you and will be in you. I will not leave you as orphans; I am coming to you. (John 14:16-18 HCSB)
But the Counselor, the Holy Spirit - the Father will send Him in My name - will teach you all things and remind you of everything I have told you. (John 14:26 HCSB)

The Holy Spirit will glorify Jesus.
He will glorify me, for he will take what is mine and declare it to you. (John 16:14 ESV)

Jesus does not need a visible Vicar.
Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed. (John 20:29 KJV)

Jesus is present on earth. Jesus is the invisible Holy Spirit. No vicar is needed.
Now the Lord is that Spirit: and where the Spirit of the Lord is, there is liberty. (2 Corinthians 3:17 KJV, NASB)

Jesus is the Mighty God and God the Father.
For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counseller, The mighty God, The everlasting Father, The Prince of Peace. (Isaiah 9:6 KJV)

Confusing? Because God is One. The Father is God. The Son is God. The Holy Spirit is God. And there is one God.

I cannot find any verse in the Bible that says Jesus needs a visible vicar on earth. I cannot find any verse in the Bible that describe the office of the vicar of Christ. The Bible tells me that God can do His job without a visible vicar. "blessed are they that have not seen, and yet have believed. (John 20:29 KJV)" So what is the visible vicar for? To remove our blessing?