Can Ted Cruz run for President?

Last I have heard, you have to be American born to be President and the news kept saying that Ted Cruz was born in Canada.
So has the rules for Presidency changed?

During the whole shut down, there have been different news stations actually have people who would comment and say that Ted Cruz is setting up to run for Presidency.

So has the rules changed or is the world going stupid? (I’m pretty sure it is the second one, but you never know?)
Or maybe this is just a Halloween Eve story?