Actually, the Constitution states that the president must be a NATURAL-BORN citizen. Children born to American parents abroad are NATURALIZED because their parents are Americans, but to be NATURAL-BORN you have to be born in the United States (or within a foreign property which is considered the United States, such as a military base).
This article explains it:
https://www.washingtonpost.com/opinions/ted-cruz-is-not-eligible-to-be-president/2016/01/12/1484a7d0-b7af-11e5-99f3-184bc379b12d_story.html