Yes. Those are the words of Christ. “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.” Mat 6:18
“The New Testament contains five different metaphors for the foundation of the Church (Matt. 16:18, 1 Cor. 3:11, Eph. 2:20, 1 Pet. 2:5–6, Rev. 21:14). One metaphor that has been disputed is Jesus Christ’s calling the apostle Peter "rock": "You are Peter, and on this rock I will build my Church, and the gates of hell will not prevail against it" (Matt. 16:18).
Some have tried to argue that Jesus did not mean that his Church would be built on Peter but on something else. Some argue that in this passage there is a minor difference between the Greek term for Peter (Petros) and the term for rock (petra), yet they ignore the obvious explanation: petra, a feminine noun, has simply been modified to have a masculine ending, since one would not refer to a man (Peter) as feminine. The change in the gender is purely for stylistic reasons.
These critics also neglect the fact that Jesus spoke Aramaic, and, as John 1:42 tells us, in everyday life he actually referred to Peter as Kepha or Cephas (depending on how it is transliterated). It is that term which is then translated into Greek as petros. Thus, what Jesus actually said to Peter in Aramaic was: "You are Kepha and on this very kepha I will build my Church." http://www.catholic.com/tracts/origins-of-peter-as-pope
Nah ... “this rock” refers to the truth Peter had just spoken. Of course, you’d have to read that verse in context to understand that ...
What was Jesus so excited about in the verse immediately preceding the one you referenced? Jesus was excited that Peter recognized Him as “the Christ, the Son of the living God.”
Jesus was excited about this truth about Himself being professed. He wasn’t particularly excited about identifying someone ELSE as the rock. Peter just acknowledged THE ROCK, and Jesus affirmed that acknowledgement.
OK, you be part of a church with Peter as the rock. I’ll claim membership in the church that has Jesus as the rock.