No, three players can kick the ball. One is the quarterback. It doesn't happen often. But can and does happen. Quarterback punting -- Ben Roethlisberger did this on November 2013. At Cleveland’s 29 yard line, because a field goal try would be 47 yards into a fairly stiff wind. Tom Brady did this January 2012 when playing the Colts.
Quarterback kicking for points -- Doug Flutie(?) did a drop-kick for one point. First time done since the 1940s, I think. So three players can kick in USA football games.