He's as American as Obama or McCain.
No question about Obama, Hawaii became a state in 1959, as for McCain, one can argue Congress cannot "add" miltary bases in foreign countries as places for "natural born" Americans, but that arugument has lost in courts.
No question Cruz is ineligible.
Cruz is indeed eligible. The fact that he did not have to go through a naturalization process, and was an automatic American Citizen at birth, makes him a natural born citizen.
Status as a natural-born citizen of the United States is one of the eligibility requirements established in the United States Constitution for election to the office of President or Vice President. This requirement was intended to protect the nation from foreign influence.
The Constitution does not define the phrase natural-born citizen, and various opinions have been offered over time regarding its precise meaning. A 2011 Congressional Research Service report stated that
The weight of legal and historical authority indicates that the term "natural born" citizen would mean a person who is entitled to U.S. citizenship "by birth" or "at birth", either by being born "in" the United States and under its jurisdiction, even those born to foreign parents; by being born abroad to U.S. citizen-parents; or by being born in other situations meeting legal requirements for U.S. citizenship "at birth". Such term, however, would not include a person who was not a U.S. citizen by birth or at birth, and who was thus born an "alien" required to go through the legal process of "naturalization" to become a U.S. citizen.
Natural-born-citizen clause - Wikipedia, the free encyclopedia
Also from the article:
Ted Cruz[edit]
Ted Cruz (born 1970), a Republican United States Senator from Texas, has publicly expressed interest in running for president in the 2016 United States presidential election.[114][115] Cruz was born in Calgary, Alberta, Canada,[116] to a "U.S. citizen mother and a Cuban immigrant father".[117] Although there are some uncertainties about the exact definition of "natural born citizen", Professor Chin (see above)
believes that Cruz
likely qualifies for the office.[117]
Cruz needs to get a declaratory Judgement, which will end the question. Arthur was "rumored" to be born in Canada, changed hus YEAR of birth to claim "natural born" status

Chester A. Arthur[edit]
Chester A. Arthur (1829–1886), 21st president of the United States, was rumored to have been born in Canada.[65][66] This was never demonstrated by his Democratic opponents, although Arthur Hinman, an attorney who had investigated Arthur's family history, raised the objection during his vice-presidential campaign and after the end of his presidency, publishing a book on the subject.[67] Arthur was born in Vermont to a Vermont-born mother and a father from Ireland, who was naturalized as a U.S. citizen in 1843, 14 years after Chester was born. Despite the fact that his parents took up residence in the United States somewhere between 1822 and 1824,[68] Arthur additionally began to claim between 1870 and 1880[69] that he had been born in 1830, rather than in 1829, which only caused minor confusion and was even used in several publications.[70] Arthur was sworn in as president when President Garfield died after being shot.
With all the debate about Obama, born in Hawaii, giving Ctuz a pass is odd. No question he was not born in the US, did not give up "DUAL" citizenship for decades.