Who built the catholic church?

If you mean who founded the Catholic Church, then the answer would be Jesus (or, if you want a more secular answer) Peter.

In the New testament, Jesus asks his disciples "Who do you say I am". Peter answers "You are the Christ, the son of the living God". Jesus replies "Indeed, You are Peter (petros mean "rock" in greek) and upon this rock I will build my church"

Peter becomes the first Pope.

The above is from a religious viewpoint. From a historical standpoint it can be said that the followers of Jesus in Jerusalem (in the first century) started a movement that solidified at the First Council of Nicaea in 325 A.D.

This council united (more or less) all the branches of what we call Christianity. The council was called by Emperor Constantine I.

So, from a historical (rather than purely religious viewpoint) you can say the Catholic church was built by Constantine I.