What is another word for crack a joke?
Pronunciation: [kɹˈak ɐ d͡ʒˈə͡ʊk] (IPA) 
There are a plethora of phrases that could be used to replace the phrase "crack a joke," each with their own unique connotations. One could say "tell a funny story," "make a wisecrack," "deliver a punchline," "spit out a one-liner," or "crack a jest." Another option might be "share a humorous anecdote," "throw out a hilarious quip," "make a comical remark," or "drop a joke." The possibilities are endless, and the choice of phrasing will depend on the situation, audience, and personal style of the speaker. Nevertheless, whatever phrasing is chosen, the goal remains the same- to bring levity and laughter to the listener.
