District of Columbia National Guard College Access Act - Amends Federal armed forces provisions to authorize the Secretary of the military department concerned to provide financial assistance to an eligible member of the District of Columbia National Guard for expenses while enrolled in an approved institution of higher education in a degree, certificate, or other program leading to a recognized educational credential at such institution. Requires such members, in order to be eligible, to: (1) be such a member for at least 12 consecutive months preceding commencement of the assistance; (2) be enrolled or accepted for enrollment at such an institution; and (3) if already enrolled, maintain satisfactory progress in a course of study in accordance with requirements of the Higher Education Act of 1965. Prohibits assistance amounts from exceeding $2,500 per academic year and $12,500 altogether.