c. 1200, "to irritate, annoy, provoke," from Old Norse angra "to grieve, vex, distress; to be vexed at, take offense with," from Proto-Germanic *angaz (source also of Old English enge "narrow, painful," Middle Dutch enghe, Gothic aggwus "narrow"), from PIE *anghos, suffixed form of root *angh- "tight, painfully constricted, painful."
In Middle English, also of physical pain. Meaning "excite to wrath, make angry" is from late 14c. Related: Angered; angering.