Hertford College sent out rejection emails, but included copies of letters with the names, addresses and subjects of all the failed candidates.
The college was quickly told, Principal Will Hutton said, and asked recipients to delete the original email.
About 200 letters were sent out from the college's senior tutor.
Mr Hutton, the writer, broadcaster and political economist, said in a statement: "We would like to apologise to all applicants affected by this mistake for any distress caused.
"We are now taking steps to make sure this type of error involving personal information does not happen again."
An Oxford University college has apologised after sending rejected potential undergraduates details of all their fellow unsuccessful applicants.