Researchers believe that when the moon is in its full or new phase that its tidal pull places more stress on the fault lines. During three of the most recent earthquakes in 2004, 2010, and 2011 were during the peak tidal stress. The researchers are not saying that this is what did cause the quakes, but it could have been the cause. Most believe that this is a coincidence not a trend with the moon phases. The moon tidal stress may cause a slight move in the tectonic plates but only about 1% or less.
Since earthquakes happen at random times its hard to say if the moon really can cause them.