Walls committed the offences at an away match against Kilmarnock
The controversial Famine Song sung by some Rangers fans is racist, appeal court judges have ruled.
The Justiciary Appeal Court upheld a conviction against William Walls over his conduct at a Rangers away match against Kilmarnock last year.
The 20-year-old's defence counsel, Donald Findlay QC, had argued the song was free speech.
But Lord Carloway said the lyrics called on people to leave Scotland because of their racial origins.
Walls was found guilty of breach of the peace, aggravated by religious and racial prejudice, at Kilmarnock District Court in December.
The offence related to his behaviour at Rangers' away match at Kilmarnock on 9 November, where he sang the Famine Song.
Rangers has asked fans to not to sing the song, which refers to the famine that killed an estimated one million people in Ireland in the 1840s.
Last month, Walls launched a appeal against his conviction.
He was represented by Rangers' former vice-chairman, Donald Findlay, who resigned from the Ibrox club in 1999 after he was filmed singing sectarian songs.
During the appeal, Mr Findlay argued that a football match was "an organised breach of the peace" and for many supporters "an exchange of pleasantries in the form of abuse is part and parcel of going to the game".
He also argued that the Famine Song - which contains the chorus "the famine is over, why don't you go home" - was not racist, but an expression of political opinion permitted under the European Convention on Human Rights.
But Lord Carloway, who heard the appeal with temporary judges Alastair Dunlop QC and Brian Lockhart QC, said: "Presence inside a football stadium does not give a spectator a free hand to behave as he pleases. There are limits and the appellant's conduct went well beyond those limits."
Referring to the Famine Song, the senior judge said: "The court does not consider that the lyrics of this refrain bear any reasonable comparison to those of 'Flower of Scotland' or indeed 'God Save the Queen'.
"Rather they are racist in calling upon people native to Scotland to leave the country because of their racial origins. This is a sentiment which... many persons will find offensive."
Lord Carloway added that the appeal judges had no difficulty in accepting the sheriff's conclusion that singing the song's chorus "displays malice and ill-will towards people of Irish descent living in Scotland".