The BRAVEHEART star has become the subject of an electioneering website boasting an online petition begging him to stand for office next year (06) - despite Gibson never having voiced a desire to enter politics.
Schwarzenegger's poll ratings have plummeted in recent weeks after a succession of ballot losses and the controversial appointment of a Democrat as his chief of staff.
MIKE SPENCE, mastermind of the Gibson internet campaign and president of the state's Republican Assembly, says, "We have to look for alternatives to the governor because he's been behaving like someone who wants to go back to Hollywood."
And Spence is eager to see Gibson as that replacement, praising the political credentials of films like The Passion Of The Christ and his outspoken views on stem cell research.
He adds, "He's shown himself to be both fiscally and socially conservative, and the success of The Passion Of The Christ shows that he has the ability to reach out to people.
"We hope to meet with him and encourage him."