The two-minute clip, widely shared on social media, shows the fan waving the flag around the empty Rangers stadium.
The images are believed to have been taken just hours after the Parkhead club obtained the title of Prime Minister SPFL on Monday.
Police are currently investigating the incident.
A spokesman for Police Scotland said: “The matter has now been reported to Police Scotland and investigations are at an early stage. “
The footage comes after Celtic tied the record for the consecutive number of titles won, after SPFL clubs unanimously agreed to end the league season at the start of the coronavirus pandemic.
Celtic’s nine consecutive accomplishments correspond to the club’s previous record set in the 1963-74 season, in addition to the ninth consecutive season for the Rangers in 1996-97.
The clip shows the Hoops fan parading a flag paying tribute to the victory of nine consecutive ranks in a provocation to the Rangers.
He can be seen walking carefully towards the central circle in case he is spotted by security guards working at the stadium.
After waving the flag for a short period of time, the chancellor then quickly rushes to his way out of the stadium.
As he runs from the field, he shows viewers where he has managed to sneak into the stadium.
He said, “Look, the little door opens here. “
“They’ve probably already phoned the brass.
“I hope I don’t get caught coming here. I’ll f ***** g make a screw or two.
“You see. “
Instead of leaving where he entered, he tries to walk through the doors of the club at a corner of the stadium.
He said, “Cannae gets up this shit end.
“How do I get oot, How do I get oot.” F ***. “
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His phone then fell to the floor as the awkward Celtic fan struggled to climb over the doors.
The Rangers have been approached for comment.