Footage shared on social media showed the fan berating a group of children before the Europa League tie against Shkupi on Tuesday, which ended 0-0.
The video ends with a man shouting ‘white power’ to the children, and was allegedly filmed before the game.
A club statement said that Rangers will ‘take the appropriate steps’ to deal with the behaviour.
It said: “This kind of behaviour is unacceptable and Rangers have been in touch with Police Scotland.”
Police Scotland said that they brought the footage to the attention of the Macedonia authorities and are ‘providing assistance’ in the investigation.
Show Racism the Red Card, a charity which deals with racism in football, told the BBC that they “are disgusted by the racism and dehumanisation” in the video.