"to bend, twist, distort," Old English weorpan "to throw, throw away, hit with a missile," from Proto-Germanic *werpanan "to fling by turning the arm" (source also of Old Saxon werpan, Old Norse verpa "to throw," Swedish värpa "to lay eggs," Old Frisian werpa, Middle Low German and Dutch werpen, German werfen, Gothic wairpan "to throw"), from PIE *werp- "to turn, wind, bend" (source also of Latin verber "whip, rod"), from root *wer- (2) "to turn, bend."
Connection between "turning" and "throwing" is perhaps in the notion of rotating the arm in the act of throwing; compare Old Church Slavonic vrešti "to throw," from the same PIE root. The meaning "twist out of shape" is first recorded c. 1400; intransitive sense is from mid-15c. Related: Warped; warping.
"threads running lengthwise in a fabric," Old English wearp, from Proto-Germanic *warpo- (source also of Middle Low German warp, Old High German warf "warp," Old Norse varp "cast of a net"), from PIE *werp- "to turn, bend" (see warp (v.)). The warp of fabric is that across which the woof is "thrown." Applied by 1947 in astrophysics to the "bending" of space-time, and popularized in noun phrase warp speed (for faster-than-light travel) by the 1960s U.S. TV series "Star Trek."