Ronaldo was booked after the referee ruled he had dived to try to win a penalty although television replays suggested the Portugal forward had been felled by a Rayo defender.
It was the league top scorer's fifth yellow and means he will miss Saturday's game at home to Eibar if the appeal fails.
"Real Madrid will appeal the yellow card that Cristiano Ronaldo received in the game yesterday," the club said on their website on Thursday.
With a win against La Liga debutants Eibar, second-placed Real can close to within a point of leaders Barcelona who play at Sevilla later on Saturday.
(Reporting by Iain Rogers, editing by Tony Jimenez)
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