A carrot riddle is:
Q: What’s orange and sounds like a parrot?
A: A carrot.
The riddle was posted on the newsgroup eunet.jokes on April 24, 1990, where it was called an old joke. The joke is that “sounds like a parrot” might imply an animal, but actually meant a word that sounds like “parrot.”
Google Groups: eunet.jokes
Ah the old ones are the best....
Stuart D Nicol MATHS87
Apr 24, 1990, 2:51:02 PM
Q : What is bright orange and sounds like a parrot ?
A : A CARROT !!!! 
13 December 1998, Mail on Sunday (London, UK), Richard Grant column, pg. 31:
WHAT’S orange and sounds like a parrot? A carrot.
Newspapers.com
7 July 1999, Home News Tribune (New Brunswick, NJ), “It’s a joke!,” pg. D8, col. 6:
Q: What is orange and sounds like a parrot?
A: A carrot!
Google Books
November 1999, Boys’ Life, “Think & Grin,” pg. 65, col. 3:
Jack: What’s orange and sounds like a parrot?
Joe: No clue.
Jack: A carrot! — Aaron Fisher, Bluefield, Va.
Twitter
the.effing.librarian
@effinglibrarian
Joke.: What’s orange and sounds like a parrot?A carrot.courtesy of Jester 4.0.This joke reminded .. http://tinyurl.com/27zb8r
7:28 PM · Oct 26, 2007·Twitter Web Client
Reddit—Dadjokes
Posted by u/BintCabinets May 20, 2013
What is orange and sounds like a parrot?
A carrot.
Reddit—Dadjokes
Posted by u/OzziesUndies July 18, 2018
What’s orange and sounds like a parrot?
A carrot
Reddit—Cleanjokes
Posted by u/Drew_Sife December 23, 2018
What’s orange and sounds like a parrot?
A carrot 🥕
Reddit—Dadjokes
Posted by u/tvz32 January 8, 2021
What is orange and sounds like a parrot?
Carrot
Reddit—Cleanjokes
Posted by u/turboshot49cents March 21, 2021
What’s orange and sounds like a parrot?
A carrot.
Above, a 1934 plaque from the Big Apple Night Club at West 135th Street and Seventh Avenue in Harlem. Discarded as trash in 2006. Now a Popeyes fast food restaurant on Google Maps.
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Above, Big Apple Corner at 54th Street and Broadway in Manhattan. Google Maps.
Above, John J. Fitz Gerald, from the Aug. 15, 1931, Binghamton (NY) Press, pg. 14.
Listen to Robert Emmerich introduce "The Big Apple," a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.
Also listen to a 1937 "The Big Apple" song by Ozzie Nelson and his Orchestra. See a 1929 photo of John J. Fitz Gerald and a 1931 photo of John J. Fitz Gerald.
This site is edited by Barry Popik.