Here.
The story tries to make hay with his claim to being offered a full scholarship at West Point when there isn't any such thing "per se", but admits that with an appointment "all costs are covered". Carson was evidently encouraged to apply by General Westmoreland at some point based on his qualifications and interest, but declined to do so in favor of a medical education.
Carson's story may stretch the facts and err in details but overall remains a plausible if understandably biased retelling of his ROTC experience in high school.
Who would fault a poor black kid from Detroit for emphasizing that a full ride through West Point had been within his reach?
Answer: the liberal hacks at Politico.