Students can rent accommodation privately and this is common in Oxford. However, do be careful that you are dealing with a reputable landlord or accommodation agency and that you have a contract. Be mindful of the length of the contract and its conditions. Sharing a property with friends or other students often means joint liability for damage and unpaid bills. The landlord is required to put the deposit in a tenancy deposit protection scheme, and they can use this to pay for any damages but should not unfairly charge for wear and tear.
Oxford Housing Group is a Facebook group which may help with finding suitable accommodation for graduate students in need of Oxford accommodation. Oxford SU (Oxford University Student Union) also provides accommodation information and a Living out Guide which students may find useful. For further information see https://www.oxfordsu.org/wellbeing/student-advice/accommodation-looking/