Get Veterans a Doctor Now Act This bill authorizes the Department of Veterans Affairs (VA) to offer a contingent physician's appointment to a person who, upon completion of a post-graduate training program, completes a residency program within two years after the VA offer. Eligibility requirements for a VA physician's appointment, including a contingency appointment, are revised to require completion of a residency program rather than an internship. At least annually, the VA must ensure that a recruiter or other similar official of each Veterans Integrated Service Network (regional VA health care administrative areas) visits each allopathic and osteopathic teaching institution with a graduate medical education program within the network to recruit individuals for the Veterans Health Administration.