Messages were sent to defender Kyle Bartley and midfielder Maurice Edu on the social networking site, leading to both players expressing their sadness at the latest racial incident to occur on the social networking website.
A number of other players have been subjected to abusive tweets this season, and Bartley, on loan at the Scottish champions from Arsenal, wrote on his page: "Disappointing that in 2012 things like this are still happening. Hopefully the police will take action. Thank you all for the support."
Edu did not make a direct statement, but in response to a Tweet from United States intenational team-mate Jozy Altidore, said: "Sad day when that`s what people are tweeting."
Strathclyde Police tonight confirmed to Press Association Sport that they were looking into complaints received, saying in a brief statement: "We will pass these posts on to the relevant officers for their attention."
Rangers also voiced their unhappiness, with a spokesman telling stv: "These comments are disgraceful and we have notified the police who are now investigating the matter.
"The club will assist with all enquiries."