Chris Graham has resigned as a non-executive director of Rangers just three days after being appointed to the Ibrox board.
In a short statement on their website Rangers said: "Chris Graham has tendered his resignation as a director of RIFC. This has been accepted by the board.
Earlier this week, the Scottish Championship side said they were looking into an alleged social media post which appeared to have been made by the 38-year-old, who is a spokesman for Ibrox fans' group Rangers Supporters Trust.
Police Scotland are also making enquiries into the matter.
Rangers chairman-elect Dave King appointed Graham to the board on Tuesday, hours before their 1-1 draw with Queen of the South, claiming he was 'making good on a promise for a fans' voice among the directors'.
Later in the day, Graham issued an apology for the offending tweet, claiming his remarks were 'inappropriate'.
In a statement, he said: "Freedom of speech is one of the foundations that our country is built upon. However, with that freedom comes a responsibility to be sensitive to the views of all our nations' communities.
"This tweet did not do that. For that I apologise unreservedly. I also tweeted my support for the Muslim community during exchanges that day (the day of the Charlie Hebdo attack in Paris) but even so I accept that retweeting that cartoon was inappropriate.
"I am extremely proud to have played a part in helping Rangers to secure regime change but I have had to take this decision for my family and the club itself. I wish the current board the very best of luck going forward."
Meanwhile, the Scottish Football Association has announced that Rangers' appearance before a judicial panel disciplinary hearing into Mike Ashley's involvement at the club, originally scheduled for next Monday, has been postponed until Thursday, April 16, 'at the request of the club'.