Is it okay to send my professor humorous material? I found a one-panel comic that is relevant to the content of a course I am taking. I think my professor would enjoy it. Is it socially acceptable to send him a hyperlink to it?
If you need to ask this kind of question on Stack Exchange then the answer is no.

You're contemplating engaging with them on a personal level, which requires a some degree of a social relationship with them.  You clearly don't have that relationship.

If, on the other hand, you had a good social relationship with your professor - shared tea and cakes during your supervision meetings, say - then of course this would be appropriate, but you would know that already.