Lavinia Woodward, 24, pleaded guilty to unlawful wounding at Christ Church college after drinking heavily.
Judge Ian Pringle QC suspended her 10-month jail sentence and at an earlier hearing said he believed immediate custody would damage her career.
She has now applied for permission to take her case to the Court of Appeal.
The case prompted a debate about inequality in the criminal justice system after Judge Pringle deferred her sentence to give her a chance to prove she was no longer addicted to drugs and alcohol.
A "debate"? That's not a debate - it's a discussion that feminists are completely