Symbolism, Imagery, Allegory
If you see a full moon pop up in An American Dream, chances are quite good that some crazy stuff is about to happen.
This is established during Rojack's time in World War II. Before killing the four German soldiers, Rojack feels "the full moon giving a fine stain to the salient of [his] mood" (1.6). Immediately afterward, the moon seems to supercharge him with the energy and aggression he needs to take down the soldiers. This experience has a huge impact on Rojack, sparking his "secret frightened romance with the phases of the moon" (1.10) that continues to this day. The moon, then, represents how out of control Rojack is when it comes to violence.
The moon shows up again when Rojack is contemplating suicide. In fact, Rojack speaks to the moon and it "spoke back to [him…] telling [him] to die" (1.14). Although this once again associates the moon with death, it also connects that celestial sphere to Rojack's lack of control. Just like during the war, it's almost as if the moon is controlling Rojack's actions. It's pretty werewolf-y, minus all the extra hair and super long nails and such.
Rojack certainly believes this—that the moon runs the show—to be true. When he becomes elected as a congressman, he even decides at times "not to make a speech because it is the week of the full lunar face" (1.10). In many ways, the moon simply represents Rojack's personal brand of lunacy.
Interestingly, the very word lunacy is derived from the word Luna—another name for the moon. Throughout human history, many cultures have believed that the moon influences our actions, inspiring us do things we'd never do otherwise. In An American Dream, this mythological belief is amped up to eleven inside Rojack's head.