Yes — once every orbit
From space, the Moon turns once on its axis during each orbit around Earth. If it did not rotate, we would see different lunar faces during the month.
The Moon does rotate — once per orbit. That 1:1 match is synchronous rotation, or tidal locking. Toggle the real locked Moon against a hypothetical non-locked Moon and track the red surface marker.
The comparison above answers the two questions people most often confuse.
From space, the Moon turns once on its axis during each orbit around Earth. If it did not rotate, we would see different lunar faces during the month.
The matching periods keep nearly the same lunar hemisphere pointed toward Earth. Small librations let us see about 59% over time.
Many large moons in the solar system are tidally locked to their planets. The Earth–Moon system is a familiar example, not an exception.
Earth's gravity gradually slowed the Moon's rotation over hundreds of millions of years (tidal friction) until it locked into this 1:1 match.
Tidal locking happens throughout the solar system — many moons of Jupiter and Saturn are locked to their planets the same way.
True distance and diameter ratio.
A different consequence of the same Earth-Moon geometry.
See the real gap between Earth and the Moon, to scale.