Alcohol can definitely cause anxiety, and make anxiety worse.
I will also suggest alcohol can trigger depression - but that is a claim that is ripe for debate and not well accepted.
Alcohol can also "treat" (in the sense of suppressing symptoms) anxiety and depression, thus leading to a downward spiral since it tends to make these things worse, thus you get into the cycle of "Oh I'm feeling anxious, better have a beer - oh, now my anxiety is worse now that I have sobered up, better have more..."