Cruz was born to an American mother, so he had American citizenship at birth. Because he was born in Canada, he also had Canadian citizenship, but renounced his dual-citizenship a few years ago.
The Constitution requires the President to be a “natural-born citizen”. It doesn’t explain much more than that, but that is taken by most (including me) to mean that someone who has to go through the naturalization process to become an American citizen is barred from the Presidency (along with anyone who isn’t a citizen, of course).
Ted Cruz didn’t have to go through a naturalization process to become an American citizen; he had citizenship from birth because his mother was an American citizen, even though she was living in Canada.
By the way, this is why the Obama “birther” movement was so stupid. Because even if Barack Obama was born in Kenya (and he wasn’t), his mother was an American citizen, so he would have had American citizenship from birth without having to go through a naturalization process.