The force are appealing for witnesses following the incident, which happened on board a train between Glasgow Queen Street and Falkirk on Sunday between 8.00pm and 8.20pm.
British Transport Police said a group of Rangers football supporters are thought to have been verbally abusive to passengers.
As the abuse continued, a member of the public decided to film the incident - capturing the use of profanity and offensive language.
A British Transport Police spokesperson said: “Were you travelling on the train at the time? Officers would like to speak to anyone who may have information which could help the investigation.
“Anyone with information is asked to contact BTP by calling 0800 40 50 40 or texting 61016, with reference 561 07/10/2018”