The moons day is the same length as the lunar month (27 days 7 hours 43.2min) - that's why it always points the same face toward earth.
This isn't a coincidence, an effect called tidal friction means that gradually the Earth has slowed down the moon's rotation until it is now locked to Earth.
It does rotate a small amount because of small variation in the orbit, you can see this from small changes in the shadows on craters.