The Old Farmer's Almanac has, for many years, suggested that periods of enhanced quake activity occur when the moon "runs high" or "runs low," which is related to elevation of the moon's orbit, etc. This has been going on for many, many years.

As Chris says, it well may have a weak effect on quakes. Added stresses of any sort may make a difference in quakes...there is currently some suggestion that major typhoons in Asia might be factored into this.