Contained in this database are birth reports from U.S. Consulates abroad between the years of 1910 and 1949. The report form is called A Consular Report of Birth Abroad and is primary proof of the individual's American citizenship. To qualify, the child must have either two U.S. citizen parents with one of the parents having resided in the U.S. prior to the child's birth, or one of the child's parents must be a U.S. citizen who has resided in the U.S. for a specified number of years previous to the child's birth.
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 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
My grandson was born in London to an American father and an English mother. Son went to US consulate that day to register his son’s birth as an American natural born citizen and a US citizen passport was issued to my grandson that day. His mother also registered his birth as a British citizen that day. When grandson comes to this country, he gets in the US citizen line for entry just like all other US citizens.
“There is a procedure for a child broad to acquire birth citizenship, note I did not say natural born citizenship, just citizenship at birth.”
I personally believe that, in the era of the founders, these two terms had distinct meanings and in reality still do but most freepers think that they know that anyone who is a citizen at birth is a natural born citizen. I hesitate to even post this because saying this will probably bring out a few of those to tell me all they know about the subject.