As reported in The Scotsman, footage posted on social media apparently showed Rangers fans Argyle Street on Sunday chanting an anti-Irish song referencing the famine.
Three men, aged 19, 21 and 24, have now been arrested and charged in connection with an incident before the match.
They are due to appear at Glasgow Sheriff Court on a later date.
Chief Superintendent Mark Sutherland, divisional commander for Greater Glasgow Police Division, said: “We have made the first of what I expect to be numerous arrests following the disgraceful racial conduct shown by a minority of Rangers supporters who were making their way to Ibrox stadium on Sunday August 29.
“Three men, aged 24, 21 and 19, were arrested and charged last night, Wednesday September 1, in connection with racially aggravated offences towards a member of the public and for the singing of racist material.”
He said racist conduct will “not be tolerated” and investigations into the incident continue.
He added: “We will continue to work with Rangers FC to identify and take appropriate action against those responsible.”
The incident happened before Rangers beat Celtic 1-0 at Ibrox.
The three men arrested were released on an undertaking and are due to appear at Glasgow Sheriff Court at a later date.