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..."
Alcohol objectively causes physiological CNS depression. Whether or not it necessarily causes the mood of depression or 'major depressive disorder' as diagnosed by clinical psychologists or psychiatrists is another matter.
“Here's to alcohol: the cause of, and solution to, all of life's problems.” -Homer Simpson