I do think that the Book of Acts spells out Jesus' words that He would use Peter to get the Church started. The Acts can be divided into 2 sections: (1) Peter, (2) Paul.
After Paul's death history tells us that Peter again became more active.
However, just because Peter was the point man in getting the church started it does not follow that he started the Roman Catholic Church. That's an unsupportable leap of logic.
Which church did he start?