This sounds more like a legal than a historical question, so forgive me if I misinterpreted what you're asking: the quickest answer is yes, since Puerto Ricans have been U.S. citizens since 1917. What about someone born before 1917? Aside from being an incredibly old contender, that might be more difficult to answer (and I'm going to guess what you're after).

Arguably, still yes—a person born on foreign soil can become a U.S. president, but in reality the laws are a bit murky. According to Section 1, Article II, of the U.S. Constitution: "No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President." So all you need is to be a natural-born citizen. Unfortunately, the Constitution does not define what "natural born" means (nor has the Supreme Court ever had to rule on it).

The 14th Amendment does certify that anyone born on U.S. soil (including bases in foreign countries—John McCain was born on the Coco Solo Naval Air Station in the Panama Canal Zone and ran for president in 2008) is a natural-born U.S. citizen, thus eligible to run for president at age thirty-five. We still have no clear definition of "natural born" outside U.S. soil. 8 U.S.C. § 1101 defines "naturalized" citizens (those not eligible to run for president) as “conferring of nationality of a state upon a person after birth, by any means whatsoever.” Section 1401 lists examples of people born on foreign soil as those who are "nationals and citizens [. . .] at birth," though it doesn't use the phrase "natural born." So if a Puerto Rican were born to U.S. citizens, before 1917, in Puerto Rico, and is still kicking, then technically yes, he or she could run for president.

Technical edits: Fixed McCain's year of running and his place of birth. Teaches me a lesson not to rely on my hunches when it comes to John McCain facts.

Context edit: To clarify what I mean by the murkiness of the law: the phrase "natural born citizen" is simply never explicitly defined. If you are born on foreign soil to a U.S. citizen parent, you are a U.S. citizen at birth (8 U.S.C. § 1401). You are not a naturalized citizen, so you should be a "natural born citizen," but the lack of such written clarity leads to potential arguments either way. (For example, as someone who falls under this category, until the Supreme Court decides on the matter, I go about calling myself a natural-born citizen.)