The moon does have a rotation, but that rotation speed has matched the speed of its revolution around the Earth. It always now shows the same face towards us.
The moon has become "tidally locked". How does this happen? Well, if the Moon were off by itself in space it would have a certain rotation-rate, but the Moon is next to a much bigger body, the Earth. The Moon raises ocean-tides on the Earth but that is nothing compared to what the Earth does to the Moon. A point nearest the Earth tries to rotate away, but it is being pulled by the Earth. Naturally, other parts of the Moon are rotating TOWARDS us and are also being pulled, but they are a little bit further away, if you do the math, by the rules of gravity are being pulled a little bit less. The Earth's gravity causes drag, and over a period of many hundreds of years, the Moon lost rotation relative to us, at least.