Five Rangers fans were arrested at Saturday's match against Kilmarnock, including one for a sectarian breach of the peace.
Two other supporters were arrested for regular breaches of the peace and two for alcohol-related offences.
The arrests followed reports of sectarian chanting and singing at the ground during the Scottish Premier League game that the club lost 1-0.
The SPL is now awaiting a match report into the behaviour of fans and has sanctions to hand if rules are found to have been broken.
This may include a financial penalty on the already struggling club.
An SPL spokesman said: "Our match delegate was at the game and will provide a report on the match early next week.
"In any breach of SPL rules, there are a wide range of sanctions available to us to impose on a club."
The Catholic Church condemned supporters for promoting "poisonous bigotry".
Church spokesman Peter Kearney said: "Despite repeated efforts by the club – and to their great embarrassment – anti-Catholic hostility is still alive and well among many Rangers fans."
Dave Scott, of anti-bigotry charity Nil By Mouth, said: "This was a day when some Rangers fans came to show their true feelings for their club. I suspect any true supporter will be sickened that others have chosen this day of all days to dredge up these songs of hate and ignorance."
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