A “Texas penny” is a $100 bill. The slang originated with the “Marge’s Son Poisoning” episode of the animated The Simpsons television show on November 13, 2005. A rich Texan (according to the stereotype, all Texans are rich from oil money and “everything’s bigger in Texas”) bets a “Texas penny” ($100) in an arm-wrestling match with Moe.
 
The term “Texas penny” has had very limited usage and usually is recalled only in reference to the television episode.
 
   
Simpsons Wiki
“Marge’s Son Poisoning” is the fifth episode of The Simpsons’ seventeenth season. It aired November 13, 2005 on FOX.
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This gives Moe an idea. When the Rich Texan man enters the bar, Homer pretends to be a nerd, and shows off his wimpy left arm. Moe tells the Rich Texan he’ll bet a hundred dollars that Homer can beat him in an arm wrestling fight. When the Rich Texan realizes he’s been conned, he demands several favors, including a walk on the beach.
 
Simpsons Wiki: Made-up words
Texas Penny
A hundred dollar bill. When Moe bets the Rich Texan a hundred dollars on whether Homer can defeat him in an arm-wrestling contest, the Rich Texan throws his hundred dollar bill on the bar and claims it is a Texas penny.
 
Zillia and the Comics Junkies
10 December, 2005 23:33,  zilla said…
you can bet a texas penny on it my friend.
 
The Online Slang Dictionary
Texas penny
noun
a $100 bill.
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Last edited on May 17 2011. Submitted by Joe H. from Mishawaka, IN, USA on Jun 29 2006.
   
Urban Dictionary
texas penny
one hundred American dollars
Moe: I bet you a hundred dollars I can beat you at arm wrestling
Texan: A Texas penny it is.
by lance… Apr 25, 2008