Old English creopan "to move the body near or along the ground as a reptile or insect does" (class II strong verb; past tense creap, past participle cropen), from Proto-Germanic *kreupanan (source also of Old Frisian kriapa, Middle Dutch crupen, Old Norse krjupa "to creep"), perhaps from a PIE root *g(e)r- "crooked" [Watkins].
From c. 1300 as "move secretly or to evade detection," also "move slowly, feebly, or timorously." In reference to imperceptible movements of things (soil, railway rails, etc.) from 1870s. Related: Crept; creeping.