1
general::
Make a joke, say something humorous, as in You can count on Grandpa to crack a joke on every occasion. This expression uses the verb to crack in the now obsolete sense of "briskly pronounce" or "boast." [Early 1700s]
American Heritage Idioms
2
general::
Phrase(s): crack a joke
to tell a joke. • She’s never serious. She’s always cracking jokes. • Every time Tom cracked a joke, his buddies broke up laughing.
McGrawhill's American Idioms And Phrasal Verbs