All nations of the world recognize jus sanguinus, the 'right of blood'. It means that you have the citizenship of your parents, no matter where you are born. Ted's mother was a U.S. citizen at the time of his birth, granting him automatic U.S. citizenship upon birth. (His father was technically Cuban at the time, though also a political refugee. I don't know if Cuba then or now recognizes his Cuban citizenship, but it's not relevant here. He later nationalized as a U.S. citizen.)

The requirements for president and vice-president are a little narrower, but would seem to adequately apply here. Since his original citizenship has never been in question, the fact that he was born outside of U.S. territory should not disqualify him, as I understand it.

There's been some talk that he should (or will) formally disclaim Canadian citizenship. That is silly and unnecessary. Unlike the U.S., Canada does not recognize jus soli ('right of the soil'), so being born in Canada doesn't confer anything like Canadian citizenship. And since neither of his parents were Canadian citizens at the time (or have ever been), he also does not qualify for jus sanguinus under Canadian law. Canada does not recognize him as one of their own in any way, shape, or form. Nor does U.S. law. So there is nothing to disclaim. If he does this, it's only to appease those potential voters who either cannot understand this, or refuse to accept it, for whatever reason. (It's kind of like those needless provisions in some states' same-sex marriage laws assuring clergy that they're exempt -- even though they're already guaranteed exemption under the U.S. Constitution.)

Prior similar examples include Al Gore (born in D.C. rather than in a 'state'), Chester A. Arthur (born in Canada, but to a U.S. mother), Christopher Schürmann (born to German citizens, but in the U.S.), Charles Evans Hughes (born to UK citizens, but in the U.S.), Barry Goldwater (born in Arizona before it was a state), George Romney (born in Mexico, but to U.S. citizens), Lowell Weicker (born in Paris, but to U.S. citizens), and John McCain (born in the Panama Canal Zone, but to U.S. citizens). (The more recent bickering about Obama merits only acknowledgement, not discussion, as he was born on U.S. soil to at least one U.S. citizen.)

I want to make it clear that my perspective on this has nothing to do with my politics. I find it hard to imagine how a guy like Cruz could be elected dogcatcher, and I vehemently oppose pretty much everything he might ever want to do. But I am very confident that his eligibility to run for President is not in question, and I will defend his right to do so.