Wikipedia says yes but on Newtonian arguments. From general relativistic point of view Moon is not rotating but moving along geodesic trajectory. And like parallel transport of a vector (pointing to the direction of motion) on a surface of a sphere along equator, from outside it seems like rotation. So, would Moon still be rotating if we remove the Earth? Would Foucault pendulum on Moon detect its rotation?
It is really rotating, with a period of one month, according to a Foucault pendulum. That's the prediction of Newtonian gravity, and GR's prediction can't diverge much from that when the gravitational field is so weak. (Also consider that a Foucault pendulum on Earth empirically measures the length of the sidereal day, not the solar day.)