From the Department of State website:
Birth Abroad to One Citizen and One Alien Parent in Wedlock
"A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) of the INA provided the U.S. citizen parent was physically present in the United States or one of its outlying possessions for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen, is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen, is required for physical presence in the United States or one of its outlying possessions to transmit U.S. citizenship to the child.) The U.S. citizen parent must be genetically related to the child to transmit U.S. citizenship."
Ted Cruz was born on 12 Dec 1970, and attended school in the United States, so this requirement is satisfied, provided that the parents were married at the time.
But now let's play the hypothetical that he was born out-of-wedlock. What does the law say about that?
Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother: "A person born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 309(c) of the INA if the mother was a U.S. citizen at the time of the person’s birth and if the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the person’s birth. The mother must be genetically related to the person in order to transmit U.S. citizenship."
So in this case, Cruz acquires US citizenship at birth under Section 301(c) of the INA.
Oops. Meant to say Section 301(d)