In Middle English, also of physical pain. Meaning "excite to wrath, make angry" is from late 14c. Related: Angered; angering.
mid-13c., "hostile attitude, ill will, surliness" (also "distress, suffering; anguish, agony," a sense now obsolete), from Old Norse angr "distress, grief, sorrow, affliction," from Proto-Germanic *angaz (from PIE root *angh- "tight, painfully constricted, painful"). Cognate with German Angst. Sense of "rage, wrath" is early 14c.
From the sense of oppression, or injury, the expression was transferred to the feelings of resentment naturally aroused in the mind of the person aggrieved. In the same way, the word harm signifies injury, damage in English, and resentment, anger, vexation in Swedish.
The idea of injury is very often expressed by the image of pressure, as in the word oppress, or the Fr. grever, to bear heavy on one. [Wedgwood]
Old Norse also had angr-gapi "rash, foolish person;" angr-lauss "free from care;" angr-lyndi "sadness, low spirits."