A turkey riddle about a bird that can “pluck itself” is popularly told on Thanksgiving.
     
“What do you get if you cross a turkey with a banjo? A bird that plucks itself” was printed in The Guardian (London, UK) on December 21, 2002. “What do you get when you cross a turkey with a banjo? A turkey that can pluck himself!” was posted on the newsgroup Google Groups: alt.humor.puns on November 30, 2004. “What do you get when you cross a turkey with a banjo? A turkey that plucks itself” was printed in Newsday (Long Island, NY) on December 1, 2007. “What do you get when you cross a turkey with a banjo? . . . A turkey that can pluck itself” was posted on Twitter by Alan S Harrell on November 22, 2012.
   
         
Newspapers.com
21 December 2002, The Guardian (London, UK), “Weekend,” pg. 70:
What do you get if you cross a turkey with a banjo?
(Pg. 63.—ed.)
A bird that plucks itself.
   
Google Groups: alt.humor.puns
Kids Puns Of The Weak 11-30-04
Stan Kegel
Nov 30, 2004, 2:28:31 PM
(...)
What do you get when you cross a turkey with a banjo?
A turkey that can pluck himself! (GMNI Rising)
 
Google Books   
Jammin’ Jokes for Kids
By Bob Phillips and ‎Steve Russo
Eugene, OR: Harvest House Publishers
2004
Pg. 126:
Cordellia & Crosby
Cordellia: What do you get when you cross a turkey with a banjo?
Crosby: I have no clue.
Cordellia: A turkey who plucks himself!
         
Newspapers.com
1 December 2007, Newsday (Long Island, NY), “Kidsday,” pg. C12:
What do you get when you cross a turkey with a banjo?
A turkey that plucks itself.
Dari Goldman
 
Twitter
gretchen smith
@gretchen_smith
What do you get when you cross a turkey with a banjo? A turkey that plucks himself.
9:45 AM · Nov 13, 2009·Twitter Web Client
   
Twitter
Gretchen Smith
@twistedtwilight
What do you get when you cross a turkey with a banjo? A turkey that plucks himself.
9:33 AM · Nov 23, 2009·Twitter Web Client
   
Twitter
Bill Helton
@7colonel7
Corny joke…What do you get when you cross a turkey with a banjo?    A turkey that plucks itself!
12:44 PM · Dec 26, 2010·Twitter Web Client
     
11 June 2009, The Advertiser (Adelaide, Australia), “Mouthing Off” by Marty Smith, pg. 18:
If you cross a turkey with a banjo, you get a bird that plucks itself.
 
Twitter
Las Vegas Carl’s Jr
@LasVegascarlsjr
What do you get when you cross a turkey with a banjo? A turkey that can pluck himself!
7:14 PM · Nov 24, 2011·Twitter Web Client
   
Twitter
USC COCES
@USCCOCES
What do you get when you cross a turkey with a banjo player?  A bird that plucks itself! #Thanksgiving
1:20 PM · Nov 9, 2012·Twitter Web Client
     
Twitter
Alan S Harrell
@ashtexas
What do you get when you cross a turkey with a banjo? . . . A turkey that can pluck itself
12:20 PM · Nov 22, 2012·Twitter Web Client
 
Twitter
Bob Kostic
@causticbob
What do you get when you cross a turkey with a banjo?
A turkey that can pluck itself!
“Happy Thanksgiving”
7:47 AM · Nov 24, 2016·Twitter Web Client
 
Twitter
Bolla@Pharaoh_Boom·Nov 24, 2016
What do you get when you cross a turkey with a banjo?
 
Bolla
@Pharaoh_Boom
Replying to @Pharaoh_Boom
A turkey that can pluck itself 😄 #BadJokeThursday
2:15 PM · Nov 24, 2016·Twitter for iPhone
   
Yahoo! Finance
25 Hilarious Thanksgiving Jokes You’ll Eat Right Up
Kali Coleman
November 25, 2020·
(...)
16. What do you get when you cross a turkey with a banjo? A turkey that can pluck itself!
 
Reddit—Dadjokes
Posted by u/VERBERD October 28, 2022
What do you get when you cross a turkey with a banjo ?
A turkey that can pluck itself.
   
Reddit—Dadjokes
Posted by u/ProfPacific November 24, 2022
What do you get when you cross a turkey with a banjo?
A turkey that can pluck itself.
   
Twitter
Kevin Davis 🚀🚀🚀🚀🚀🚀
@kevindavis338
What do you get when you cross a turkey with a banjo?
A turkey that can pluck itself.
8:06 AM · Nov 24, 2022 from South Elgin, IL·Twitter Web App