Jamie Robertson, 28, behaved in a threatening or abusive manner at Hampden Park on April 16, 2022.
The offence took place during the semi-final of the Edinburgh Derby which Hearts won 2-1.
Court papers state Robertson crossed over a barrier and attempted to enter the field of play.
It is stated Robertson, of Dunfermline, Fife, went on to shout and swear.
READ NEXT: Teenager stabbed in shock attack in the middle of Glasgow city centre
Robertson also pleaded guilty at Glasgow Sheriff Court to assaulting police officer Ashley Robertson.
The charge says Robertson struck her head with his hand.
Lyndsey Barber, defending, will make her plea in mitigation at next month’s sentencing.
More information surrounding the circumstances will be heard.
Robertson was granted bail meantime.
