I have a switched outlet in a bedroom. The top receptacle is controlled by a wall switch while the bottom is always hot. Can I make it so the top is always hot and the bottom is switched by just moving the hot wire to the top and the red(switch) wire to the bottom?
Yes, that's exactly what you should do.
As a safety measure, while you've got the wiring exposed, double check that the hot (black and red) wires are connected to the brass-colored screw on the receptacle, the neutral (white) is connected to the silver-colored screw, and the ground is connected to the green screw.
If the bond between top and bottom is broken on the neutral side as well, switch the neutral wires as well as the hot wires. If it's not broken then switching only the hot wires is adequate. When switching off the circuit breaker(s) beware of the possibility (not common but possible) that the top and bottom are on different breakers.