Sgt Jon Harris had been sent to an alleged assault in the Waterloo Bar in Argyle Street on Wednesday night.
After dealing with the incident he surprised customers by belting out the classic 70s track on the karaoke.
Peter McKenna-Boyd, who filmed the performance, said: "Everybody just loved it".
The officer was in full uniform at the time.
Mr McKenna-Boyd told BBC Radio Scotland's The Kaye Adams programme: "Nobody expected it to happen. It was just a normal Wednesday night for us.
"They've just launched their new wacky Wednesday which is a bit of a game show and a bit of karaoke."
"I think the sergeant was speaking to the karaoke host and she suggested he got up to sing but I don't think she expected him to," Mr McKenna-Boyd said.
"But she held him to it just before he went out the door. The other officers were outside and they heard his name called up and they ran straight back in.
"They loved it as well. Everybody was clapping and cheering for him.
"He was hilarious, especially his pointing and his dance moves. The other policemen were standing and clapping and cheering. Not sure if he was their boss but when they first saw him it was like their dad had just got up on the karaoke."
Ch Insp Mark Sutherland, of Police Scotland, said: "Around 19.10 hours on Wednesday evening, officers were called following an alleged assault within the Waterloo Bar on Argyle Street in Glasgow city centre.
"A full and thorough investigation led to the arrest of a 23-year-old male who is expected to appear at Glasgow Sheriff Court on 2nd June.
"Once the inquiry had concluded and the victim's safety ensured, Sgt Jon Harris from our city centre community policing team was encouraged to participate in karaoke ongoing in the pub. 'Sgt Jon' took to the stage which helped to defuse any simmering tensions in the pub.
"I was pleased to see that once the incident had been professionally concluded, my officers were able to share a lighter moment with those who remained in the pub."
A police sergeant called out to deal with a brawl in a Glasgow pub ended up giving an arresting performance of Gloria Gaynor's I Will Survive.