The state department doesn’t think its quite that simple.
They say that if the paperwork is in order...
“A child born abroad to a U.S. citizen parent or parents may acquire U.S. citizenship at birth if certain statutory requirements are met. The child’s parents should contact the nearest U.S. embassy or consulate to apply for a Consular Report of Birth Abroad of a Citizen of the United States of America (CRBA) to document that the child is a U.S. citizen. If the U.S. embassy or consulate determines that the child acquired U.S. citizenship at birth, a consular officer will approve the CRBA application and the Department of State will issue a CRBA, also called a Form FS-240, in the child’s name.”
This is the documentation they require
http://www.state.gov/documents/organization/156216.pdf
If Ted Cruz’s parents did obtain citizenship for him at birth he is golden. If not and he obtained it when his father became a US citizen we are back in the morass of natural born vs naturalized. He was born in Canada to a Canadian citizen Dad with a Canadian BC, a natural born Canadian citizen. If his Mom was a US citizen at that point she could have filed to have him declared one as well.
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 the genetic or the gestational parent and the legal parent of the child under local law at the time and place of the child’s birth to transmit U.S. citizenship.
Going to 301(c) of the Immigration and Nationality Act (INA)
D. Application for Certificate of Citizenship (Form N-600)
A person born abroad who acquires U.S. citizenship at birth is not required to file an Application for Certificate of Citizenship (Form N-600). A person who seeks documentation of such status, however, must submit an application to obtain a Certificate of Citizenship from USCIS. A person may also apply for a U.S. Passport with the Department of State to serve as evidence of his or her U.S. citizenship. [14] See 8 CFR 341.1. The Secretary of State has jurisdiction over claims of U.S. citizenship made by persons who are abroad, and the Secretary of Homeland Security has jurisdiction over the administration and enforcement of the INA within the United States. See INA 103(a)(1) and INA 104(a)(3). There is nothing precluding USCIS from accepting a Form N-600 filed under INA 301 or INA 309 by a person who does not live in the United States. See INA 341(a).