Could happen if the actor and former strong man runs for that office in the future.
The Austrian-born star admittedly has political ambitions, and the California electorate has been kindly disposed toward actors running for public office in the past.
What further proof is required than the election of Ronald Reagan to the governor's mansion in Sacramento and thereafter Reagan's election to the Presidency of the United States. Not once, but twice.
Reagan, still revered in California -- and in much of the rest of the country -- was not anywhere near as big a movie star as Schwarzenegger.
But Reagan, a victim of Alzheimer's disease and living quietly in Bel Air, was an all-American type. He is wholesome, home-bred American from Illinois.
Arnold, on the other hand, is foreign-born with a Teutonic accent you could cut with a bayonet.
All the same, there is something homespun and folksy about this star of action pictures that he shares with the former president.
If not homespun, then he has a trustworthy aura uncommon to most slick office-seekers in every culture around the planet.
Arnold is not as polished and smooth as the late actor George Murphy, who served with distinction in the U.S. Senate in the '60s, but he is considerably more dynamic.
In addition to being a performer, Schwarzenegger shares the same political philosophy with Reagan and Murphy. He is a Republican.
But that is not necessarily a good thing.
Voter registration in California is almost a 2-1 Democratic.
However, Schwarzenegger is unfazed by overwhelming odds.
He arrived in this country in 1968, a muscle-bound body-builder from Austria speaking broken English and with a vague desire to become a Hollywood actor some day.
The odds against that happening?
Ten Brazilian to zero.
From a monoglot immigrant, Arnold mastered English well enough to star in "Conan The Barbarian" in 1982 and a sequel before moving on to other starring roles.
Subsequently Schwarzenegger appeared in more than 50 feature films and television projects.
Schwarzenegger did not become just another actor; he became a movie superstar with enormous box-office clout.
He compiled a fortune from his acting roles and through wise investments, especially in Southern California real estate. Arnold now is one of the wealthiest actors in Hollywood, commanding as much as $30 million per film.
Over the years he has trimmed down his impressive physique; taken to producing his own films and opened his own restaurant along with other projects.
He is becoming more verbal and is a visible champion of children's issues,
commenting on government programs and expounding his own thoughts on the economy.
Arnold became an American citizen in 1983 and three years later married Maria Shriver, of the political Kennedy clan. They and their four children live in the posh Los Angeles suburb of Pacific Palisades. They vacation in a vast mountain mansion in Sun Valley, Idaho.
Schwarzenegger graduated from the University of Wisconsin in 1989, where he majored in international marketing and business administration.
Of late Schwarzenegger has fashioned his image as a devoted family man with interests in social progress and a desire to improve the status quo.
He supports women's rights, abortion and other issues that do not exactly please mainstream Republicans.
It would appear that Schwarzenegger is not as politically conservative as Reagan and Murphy, but he is cautious about endorsing any programs that might prove embarrassing if he announces his candidacy in 2006.
Political pundits aver that if Republican Bill Simon, underdog in this year's gubernatorial race, wins the election, Schwarzenegger may shift his focus to a U.S. Senate seat.
The cigar-smoking Schwarzenegger is an affable man, cautious about wading into perilous political waters. He is reluctant to discuss his political plans until he is better prepared to handle the media.
Unlike Reagan and Murphy, Arnold has not been active in show biz politics. Both the others were president of the Screen Actors Guild before setting their sights on professional politics.
Schwarzenegger is essentially an optimist, and why not? He came to this country an impoverished body-builder and has become a multimillionaire and international celebrity.
Who would have thought, for instance, that Grace Kelly would have become a European princess and Ronald Reagan, who starred in "Bedtime for Bonzo," would become President of the United States?
Then there's the case of Minnesota Gov. Jesse Ventura, a professional wrestling gonzo with far less charisma than Conan, the Terminator and other heroic characters Arnold has played.
It helps Schwarzenegger's political aspirations that he exudes charm, sincerity and genuine interest in the people he meets.
Perhaps his greatest asset is that Schwarzenegger, like Reagan, is unwilling to be content with simply being a movie star.