Bartholomeo Joly de Lotbiniere, 21, was on trial at York Crown Court over an alleged incident at a halls of residence in June 2014.
After deliberating for almost 10 hours, the jury of eight men and four women was unable to reach verdicts on a charge of rape and indecent assault which the defendant denied.
Judge Paul Batty gave the Crown Prosecution Service a week to consider whether it will seek a retrial. The case will be listed again on Thursday next week for an administrative hearing.
The complainant had told the jury that Joly de Lotbiniere went into her room after they had been on a night out and then raped her as she tried to push him off. She went to the police more than a year on from the alleged offence after Joly de Lotbiniere appeared on University Challenge, representing the University of York.
The defendant, of Kensal Rise, London, said what happened between them was consensual, and described it as a “failed one night stand”. He told the jury he was sexually inexperienced. Joly de Lotbiniere is now studying for a Masters degree at University College London.