"to utter the call or cry of a hen," Old English cloccian originally echoic. Compare Turkish culuk, one of the words for "turkey;" Greek klozein, Latin glocire, German glucken. Related: Clucked; clucking.
1703, "sound made by a hen," from cluck (v.). Slang meaning "stupid person" (chickens and turkeys are famously foolish) is from 1927.