late 13c., from Old French oncle, from Latin avunculus mother's brother, literally little grandfather, diminutive of avus grandfather, from PIE root *awo- grandfather, adult male relative other than one's father (cf.
http://www.dictionary.com/browse/cry--uncle
Say uncle is sometimes claimed to come from the Irish anacol, meaning mercy or quarter, the lack of currency in Britain explained by the term being brought to America by Irish immigrants. Despite the similarity in sound and meaning, there is no strong evidence to support this conjecture.
http://www.wordorigins.org/index.php/site/say_uncle/
1250-1300; Middle English < Anglo-French uncle, Old French oncle < Latin avunculus mother's brother, equivalent to av(us) mother's father + -unculus suffix extracted from diminutives of n-stems (see homunculus)
http://www.dictionary.com/browse/cry--uncle
This phrase originated about 1900 as an imperative among school-children who would say, “Cry uncle when you've had enough (of a beating).” By the mid-1900s it was being used figuratively, as in the examples.
http://www.dictionary.com/browse/cry--uncle
Sic him Jenny Jinx—make him say ‘Uncle’. The phrase may come from the punchline of a joke that was popular in the 1890s. Douglas Wilson (one of this site’s regulars) discovered this version of the joke in the Iowa Citizen, 9 October 1891: A gentleman was boasting that his parrot would repeat anything he told him.
http://www.wordorigins.org/index.php/site/say_uncle/
The phrase may come from the punchline of a joke that was popular in the 1890s. A gentleman was boasting that his parrot would repeat anything he told him. For example, he told him several times, before some friends, to say “Uncle,” but the parrot would not repeat it.
http://www.wordorigins.org/index.php/site/say_uncle/
Dutch oom, Old High German oheim maternal uncle, German Ohm uncle). Also from French are German, Danish, Swedish onkel. First record of Dutch uncle (and his blunt, stern, benevolent advice) is from 1838; Welsh uncle (1747) was the first cousin of one's parent. To say uncle as a sign of submission in a fight is North American, attested from 1909, of uncertain signification.
http://www.dictionary.com/browse/cry--uncle
Slang with 90+ answers. The first recorded example of say uncle, also found as cry uncle, and meaning to beg someone to stop an action, or, intransitively, to surrender, is this: 1916 Literary Digest vol.
https://www.quora.com/Where-did-the-phrase-Say-Uncle-come-from
The speculations are ingenious: one from American Speech in 1980 was that “Uncle in this expression is surely a folk etymology, and the Irish original of the word is anacol ... ‘act of protecting; deliverance; mercy, quarter, safety’, a verbal noun from the Old Irish verb aingid, ‘protects’ ”.
http://www.worldwidewords.org/qa/qa-say1.htm
It is possible to conjecture that the popularity of this joke lead to the phrase Say 'uncle', Cry Uncle' and the like for situations where one person is trying to bend another to their will. Daniel McLaury, knows over 100 different words.
https://www.quora.com/Where-did-the-phrase-Say-Uncle-come-from
where did crying uncle originate
Crying uncle originated from Irish Anacol.   Crying Uncle originated in Irish Anacol.