Green’s Dictionary of Slang

1. to beat, to thrash.

1864

Derby Day 70: ‘You won’t goat me?’ ‘I won’t touch you this time.’.

2. (US campus) to ‘pledge’ for admission to a college fraternity [? SE scapegoat, with ref. to humiliating and/or painful initiatory rites].

1950

R. Starnes And When She Was Bad 191: ‘Do you always go around rodded up, gumheel?’ he asked [...] ‘Goating for a frat,’ I said. ‘They made me do it’.

3. see get someone’s goat under goat n.¹