Porteous was dimissed on the half-hour mark by referee Nick Walsh for a challenge on Joe Aribo. The incident came at a time when Hibs were leading the match 1-0.
Hibs say they “stand united” with the 22-year-old after comments from Rangers manager Steven Gerrard branding the tackle a “leg-breaker”.
Hibs chief executive Ben Kensell said: “After reviewing footage of the incident, we have decided to appeal the decision.
“We believe we have enough evidence to show his challenge was not worthy of a sending off.
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“We will await an answer from the SFA and stand united with Ryan, who has our absolute support.”
If the red card is upheld, Porteous will be suspended for Hibs first two games after the international break at home to Dundee United on Saturday, October 16, and Aberdeen away on Saturday, October 23.