late 14c. (implied in curled), "turn, bend, form in ringlets" (transitive), a metathesized formation corresponding to the Middle English adjective crull, crulle (c. 1300), which is probably from an unrecorded Old English word or from Middle Dutch krul "curly," from Proto-Germanic *krusl- (source also of East Frisian krull "lock of hair," Middle High German krol, Norwegian krull, Danish krølle "curl").
Intransitive sense of "take the form of a curl, assume a spiral shape" is from 1520s (originally of hair). Meaning "to play at curling" is from 1715. Related: Curled; curling.
c. 1600, "a ringlet of hair;" by 1610s in reference to anything of similar spiral or undulating form; from curl (v.). Surfer slang for "curved top of a breaking wave" is by 1962.