Scott Lamont, from Glasgow, was heard singing the words of the Billy Boys song on Cathcart Road on 1 February.
The 24-year-old admitted the charge at Glasgow Sheriff Court.
He was also given an 18-month football banning order and told his behaviour would not be tolerated.
Sheriff Paul Crozier told Lamont's lawyer, Joanne Gray: "Glasgow has developed a good reputation in recent years.
"We had the Commonwealth Games last summer, we haven't had an Old Firm game in years.
"What happened at the first Old Firm game? People like him let Glasgow down."
The sheriff described the words to the song as "inflammatory" an said it "could have led to horrendous violence".
He told Lamont: "Your conduct on 1 February was the sort of conduct that the authorities had asked football loving fans to refrain from.
"A message has to be sent to those people who would choose to ruin football for the vast majority who want to go to these games, that you cannot behave like this.
"This sort of behaviour will not be tolerated, certainly not by me."
Another man, Alexander Blood, from Saltford in Somerset, was given a community payback order after admitting acting in a racially aggravated manner.
Blood swore at police officers and called them "Jock".
As part of the order he will be supervised for 18 months and must carry out 160 hours of unpaid work.
He was also given a three year football banning order.
A Rangers fan who was arrested for sectarian singing while on his way to attend a game against Celtic has been jailed for four months.