The struggling West London club said on their website that they had lodged a formal appeal and would be making no further comment.
Barton was dismissed for an off the ball incident with Norwich's Bradley Johnson after 34 minutes when he appeared to headbutt his opponent during the Premier League match at Loftus Road which Norwich won 2-1 after Barton had given Rangers an early lead.
Both Barton and his manager Neil Warnock vehemently protested the sending off after the game, with Warnock claiming that referee Neil Swarbrick and his linesman were "conned" into sending off the Rangers skipper.
"The assistant referee has guessed, if I'm honest," Warnock told BBC Sport. "Who says cheats don't prosper? Bradley has conned him."
Barton added on Twitter: "Hopefully [the] ref sees it retrospectively and sees he's been conned."
Barton said the officials told him at half-time that they "never saw" the incident with Johnson.
"I feel for the officials; they've been conned. I was pulled back first, then kicked second," Barton tweeted after his dismissal.
Rangers, back in the top flight for the first time since 1996, were ninth on November 19, but have slipped to 17th, just one place above the relegation zone, after picking up just two points from a possible 24 from their last eight matches.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
