Here is the relevant definition of citizenship at birth, according to US law:
http://www.uscis.gov/us-citizenship/citizenship-through-parents The part that pertains to Ted Cruz is here:
“A Child Born Outside the U.S. is a Citizen at Birth IF...
One parent is a U.S. citizen at the time of birth and the birthdate is before November 14, 1986 but after October 10, 1952 AND
The parents are married at the time of birth and the U.S. citizen parent was physically present in the U.S. or its territories for a period of at least ten years at some time in his or her life prior to the birth, at least five of which were after his or her 14th birthday.”