The Rangers also banned William Walls, 20, of Glasgow for life, The Scotsman reported.
Walls was caught by Rangers stewards during a match with Kilmarnock in November singing the "Famine Song." Rangers management has been trying to overcome the team's image as the favorite of sectarian Protestants and have asked fans not to sing that song and similar ditties.
The song talks about the 19th century failure of the potato crop, which killed about 1 million people in Ireland.
"The Crown Office and Procurator-Fiscal Service take all instances of racism and bigotry very seriously," said Les Brown, the prosecutor. "We will prosecute in court all offenses which are aggravated by racial or religious prejudice."
The Rangers and Celtics, both based in Glasgow and known collectively as the Old Firm, have one of the longest rivalries in the history of professional sport and one that has been nourished by religious sectarianism.