Oooh, parrot jokes! I know there are other good ones out there--anybody got any? (hint)
Believe it or not, "parrot jokes" googles to fully 470 hits -- some people have too much time on their hands!

A personal favorite is word-related, for it requires yiddish; the oft-told english punchline is IMHO far inferior. The yiddish word chachma literally means wisdom or a wise act, but more often is used with sarcastic derision. (Just as the english wise guy, though literally complementary, is a derisive term.)

A magician, on a cruise ship, regularly had his routines ruined by the onboard parrot, who would fly around squawking out his secrets. "IT'S UP HIS SLEEVE!", the parrot would squawk, or "IT'S BEHIND THE SCREEN!", or "THERE'S A FALSE BOTTOM!"

One night during a frightful storm at sea, the magician was giving the performance of his life in an attempt to distract the frightened passengers -- subject to he parrot's usual interference. Suddenly a tremendous wave smashed the ship in two, and all found themselves thrashing in the water, in chaos. As the magician clung to a scrap of wood for dear life, the parrot eventually drifted by him in the random currents. The parrot, fixing a skeptical eye upon him, asked disdainfully:

yiddish version: So tell me, vas dis trick chachma?
english version: OK, I give up. What did you do with the ship?