Ted Cruz was definitely a U.S. citizen at birth.
It is possible for U.S. citizen parents to transmit citizenship to their children depending on when the child was born and when the parents lived in the United States.
If the applicant was born to one U.S. citizen parent and one alien parent:
The child was born between Dec 24, 1952 and Nov 14, 1986, then the U.S. citizen parent must have resided in the U.S. ten years prior to the applicant’s birth, with five of those years occurring after the parent turned 14.
If the applicant was born to one U.S. citizen parent and one alien parent:
The child was born between Dec 24, 1952 and Nov 14, 1986, then the U.S. citizen parent must have resided in the U.S. ten years prior to the applicant’s birth, with five of those years occurring after the parent turned 14.
Do you know what is a difference between this sort of citizenship and "natural born" citizenship? You don't have to get out the rule book to see if the "natural born" qualify.