Oh goody, another birther! Just keep wasting your time chasing that rabbit, my friend...
From the US State Department
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.
The procedure is as documented for US Armed forces families at military.findlaw.com but this procedure dates back to 1910 and applies to all US citizens living aboard.
From military.findlaw
If the parents are married to each other, the child is a U.S. citizen if
One parent is a U.S. citizen, and the U.S. citizen parent lived in the U.S. for at least five years prior to the child's birth, at least two of which were after the age of fourteen.
In Cruzs' case the above is applicable. Then the procedure to acquire "birth citizenship" is:
After the parents have determined that their child is a U.S. citizen, they need to apply for a Consular Report of Birth Abroad at the nearest U.S. consulate. The parents will need to submit an application (PDF), along with documentation proving the parents' citizenship and the record of the child's birth from the resident country. The Consular Report of Birth Abroad can be used later as proof of the child's U.S. citizenship, and may be used to obtain a U.S. passport for the child. -
See more at: http://military.findlaw.com/family-employment-housing/military-children-born-abroad.html#sthash.1zXFHWSD.dpuf