Can a mlb player catch a fair ball with his baseball cap?

No fielder can use any part of the uniform to catch a batted ball. In fact, if a a fielder touches a fair batted ball with his cap, mask or any part of his uniform detached from its proper place [Rule 7.05(b)], or if a fielder deliberately throws his glove and touches a fair batted ball [Rule 7.05(c)], the runner is entitled to 3 bases without liability to be put out. And it's two bases if it's a throwen ball.