I do not believe Sharia is consistent with the Constitution of this country. Muslims feel that their religion is very much a part of your public life and what you do as a public official, and that’s inconsistent with our principles and our Constitution.According to The Hill:
Carson said that the only exception he’d make would be if the Muslim running for office “publicly rejected all the tenants of Sharia and lived a life consistent with that.” ... However, on several occasions Carson mentioned "Taqiyya," a practice in the Shia Islam denomination in which a Muslim can mislead nonbelievers about the nature of their faith to avoid religious persecution. “Taqiyya is a component of Shia that allows, and even encourages you to lie to achieve your goals,” Carson said.CAIR says it will send each candidate in the primaries a copy of the Koran, and will send a copy to any American who requests it and pays the cost of shipping.