Recovering Service Members Disability Benefits Act - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act to create an exception from the required waiting period for disability insurance benefits in the case of recovering service members (of the Armed Forces, including a member of the National Guard or a Reserve component, who is undergoing medical treatment, recuperation, or therapy while recovering from a serious bodily injury or physical illness related to the member's military service).