What's up DC and hypno nerds, question for y'all. In Zatanna's wikis, almost all of them list hypnotism as one of her acquired skills. But, is there any comic or show that actually PROVES this?

I'm starting to think it's a made-up head cannon. But, happy to be proven wrong

Not sure to be honest.

Zatanna is one of the most powerful magic-users in the DC universe, so it wouldn't be impossible for her to have powers that can influence a person's mind. She has been shown the ability to mindwipe people (i.e. erase a person's memories).

In Identity Crisis she wiped the memories, and altered the personality, of Doctor Light, after the rape of Sue Dibney. She mindwiped Batman as well when he discovered what she and the League had done.

As far as mind controlling or hypnotizing people I'm not aware of any instances of Zatanna using such a power, at least not in any major story lines or cartoons.

Traditional hypnosis? I'm not sure she ever has "on-screen", although she certainly could. For Zatanna content along those themes, consider the Batman & Robin Adventure Annual #2 (1997), involving a throw-away villain called Hypnotist. Or the Smallville episode "Hex".