Can an american citizen born outside the united states run for president?
No they cannot. One of the most complicated areas of US citizenship law involves the passage of citizenship to children born outside the US to one or more US citizen parents. While naturalized US citizens are treated like natural born citizens, which includes those who are deemed citizens even when born outside the US, in almost every respect, there is one important office that only natural born citizens can hold – the presidency (though expect to see efforts in Congress to change this if Governor Arnold Schwarzenegger decides to run for President). Article II, Section 1, clause 4, of the U.S. Constitution says that “[n]o person except a natural born citizen … shall be eligible to the Office of President.” In the U.S. Code, Title 8 covers “Aliens and Nationality”. In Chapter 12, “Immigration and Nationality” of Title 8, appears Section 1401. See this link for more detail.
One thing that many people fail to understand is that Congress can decide what is considered a “natural born” citizen. A Constitutional Amendment is not required to change this…. The laws have been changing throughout the 20th century, and have already changed in the 21st Century with The Child Citizenship Act (CCA) which becomes effective on February 27, 2001, amends the Immigration and Nationality Act (INA) to provide U.S. citizenship. AND if Congress WANTS, they could grandfather in a clause for what determines “natural born”. Thus, President Arnold Scwartzenegger could, in theory occur, via Congress changing the terms of “natural born”, but most likely will not happen.