Expedited Hiring for VA Trained Psychiatrists Act of 2017 This bill authorizes the Department of Veterans Affairs to appoint a psychiatrist who completes a residency at a Veterans Health Administration (VHA) facility to a VHA health care position immediately after such residency, without regard to civil service or classification laws, if: (1) the psychiatrist meets the qualifications established in regulations prescribed for the position, and (2) the position has been unfilled for at least 35 days.