John Fordham, 21, of Dalry, North Ayrshire; and Jordan Robertson, 18, of Bishopbriggs, East Dunbartonshire, were fined a total of £600 after being found guilty yesterday at Glasgow Sheriff Court.
The pair committed the offence at a televised match between Berwick Rangers and Rangers at Shielfield Park in Berwick-Upon-Tweed on February 23 last year,
Police in the stand became aware that a number of fans were singing offensive songs. The subsequent investigation led to the arrests as the men attended other matches at Ibrox Stadium.
The Offensive Behaviour at Football and Threatening Communications (Scotland) Act 2012 allows for people who live north of the Border to be prosecuted by the Scottish authorities even if the crime took place in another country.