Were uncles so cruel to their nephews they once made them beg for mercy? How did this “convention” of yelling “uncle” get started? And did our aunt’s make them stop… :dubious: before our uncles got hurt! 
- Jinx
The origin is unknown:
“The exact origin of “say uncle” or “cry uncle,” an American invention first appearing in written English around 1918, is unclear, but there are, as usual, some interesting theories. One theory posits that “uncle” is actually a mangled form of the Irish word “anacol,” meaning “protection” or “safety,” making a demand from an aggressor to “cry uncle” equivalent to the thug demanding that his victim “cry for help” as a signal of surrender. There’s no real evidence to support this theory, but there certainly was no lack of recent Irish immigrants in the U.S. around the turn of the century, so it’s not entirely implausible.”
More theories in the link:
Perhaps it has to do with the stereotypical fellow who enjoys tickling his nieces and nephews until they beg him to stop?
Douglas Wilson over at the American Dialect Society has found a cite as early as 1891, still only in the US.