Shrug

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late Middle English (in the sense ‘fidget’): of unknown origin.

wiktionary

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From Middle English schruggen, shrukken, probably of North Germanic origin related to Danish skrugge, skrukke(“to stoop; crouch”), Swedish skruga, skrukka(“to huddle; crouch”), all from or related to Old Norse skrykkva, from Proto-Germanic *skrinkwaną. Compare also Old English scrincan(“to shrink”). More at shrink.

etymonline

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shrug (v.)

c. 1400, schurgyng, of uncertain origin. Perhaps connected to Danish skrugge "to stoop, crouch." Related: Shrugged; shrugging. To shrug (something) off "dismiss" is recorded from 1909.

shrug (n.)

a shoulder motion meant to express indifference, want of an answer, etc., 1590s, from shrug (v.).