J.R.R. Tolkien taught English Language and Literature at Merton College, Oxford.
Tolkien became the Rawlinson and Bosworth Professor of Anglo-Saxon at Oxford in 1925, then held the Merton Professorship of English Language and Literature from 1945 until his retirement in 1959. Merton College was therefore the Oxford college most directly associated with the later professorship named in his academic career.
His university work focused on languages, medieval literature, and philology, the historical study of language. His expertise in Old English, Middle English, Old Norse, and related traditions influenced the texture of his fiction. A common mix-up is to associate Tolkien’s teaching career only with Pembroke College, where he was a fellow and professor earlier in his Oxford career. The question asks specifically about the Merton professorship, not every college connection in his academic life.