Sure He does! Where else would we get ours, since we are made in His image, and a sense of humor is such a delightful gift?
Humor, though, is culturally rooted (with the exception of mother-in-law jokes, which are apparently universal in any culture on the planet!). That's why most of us Westerners find it difficult to understand that Jesus was really a funny fellow. For instance, it's easy for us to imagine Him intoning solemnly, "Blind guides! You strain out a gnat yet swallow a camel!" (Matt. 23:28) Not only is it a funny mental image, but Jesus was making a pun that is completely lost in translation. The Aramaic word for gnat is galma, and the word for camel is gamla. If we'd been there as onlookers, we would have howled.