I don’t think so. Foreign born individuals are not eligible. Vote Schwarzenegger!
Jay Parker (I) imdb
1

As long as your parents are United States citizens you are “natural born” regardless of where you are born. For example, Ted Cruz was born in Canada while his mother was a United States citizen — he is eligible to run and serve as president. On the other hand, despite however much you might want to see Arnold Schwarzenegger serve as president he was born in Austria to Austrian citizens. As a “naturalized” citizen Arnold will have to be satisfied being the former governor of California.