Not possible legally...
...as he doesn't meet the residency requirement - to be eligible to run, you have to have lived in the US for the previous 14 years at least:
"No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States."
Not that Ted Cruz is worried about the "natural born citizen" part, of course.
Biting the hand that feeds IT
