Translation from what language(s) into which language(s)?
There are a huge range of language courses available at Oxford at both undergraduate and graduate level (including most common and some uncommon European languages, as well as a range of Asian and Middle Eastern languages, and also a variety of ancient and medieval languages). These will all involve some level of translation (probably to/from English) and reading in the target language directly.
At the undergraduate level languages are mainly delivered through the modern languages (European languages) courses, AMES (for Asian and Middle Eastern languages including ancient/classical languages from those regions e.g. Sanskrit, Akkadian/Sumerian, Egyptian hieroglyphs, etc), and classics (ancient Greek and Latin). There are also various joint courses between those subjects (e.g. modern languages and AMES, classics and modern languages, classics and AMES) and with other subjects (e.g. linguistics, politics, history, religion/theology etc). Also the English language and literature course includes Old and Middle English (this is the language portion) and may have options in Old Norse and such sometimes I gather.
At the postgrad level aside from a large number of courses in those departments mentioned above, is also a masters course in comparative literature and critical translation for people with language skills in two or more languages and their literatures already. There are also more philological/text and translation based routes through the MPhil in the linguistics department if you have appropriate language skills already and are primarily interested in historical linguistics. There's also some more interdisciplinary courses in medieval studies and Byzantine studies which involve some language elements.