Yes, you can if the country where you are born recognizes jus soli - (if you are born in that country, regardless of the nationalities of your parents). The U.S. recognizes natural born citizenship if you are born here (even if neither of your parents is a U.S. citizenship) AND if you are born in another country as long as one of your parents is a U.S. citizen (and has lived here for the requisite amount of time). Canada did as well in 1970, the year Cruz was born. I don't know if Canada still does.
Before the Constitution, the closest reference we have to Natural Born Citizen is from the legal treatise “the Law of Nations,†written by Emerich de Vattel in 1758.
http://www.constitution.org/vattel/vattel.htm
In book one chapter 19 § 212. Of the citizens and natives:
“The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens.”
Natural Law is different than government law.
A natural born citizen is so because of Natural Law not government laws. Some one born on soil with two citizen parents is a natural born citizen because no other sovereign but the sovereign of the soil he was born on has any claim to his elegance.
This is not rocket science.