Underserved Veterans Access to Health Care Act - Directs the Secretary of Veterans Affairs (VA) to establish medical residency programs, or ensure a sufficient number of residency positions in medical residency programs, at VA medical facilities that the Secretary determines: (1) are experiencing a shortage of physicians, and (2) are located in communities that are designated as a health professional shortage area.

Requires the Secretary to determine the specialty of health care professionals that a location is experiencing a shortage of and allocate residency positions based on such determination.

Directs the Secretary, during the five-year period beginning on the enactment of this Act, to establish not fewer than 2,000 graduate medical education residency positions, giving priority to VA medical facilities that: (1) do not have medical residency programs, and (2) are located in communities that have a high concentration of veterans.