Restore Honor to Service Members Act This bill requires appropriate military record correction boards or discharge review boards to review the discharge characterization of any former members of the Armed Forces requesting a review who were discharged because of their sexual orientation. Such boards to change a characterization to honorable if such characterization is any characterization except honorable. The Department of Defense (DOD) shall ensure that any such changes are carried out consistently and uniformly across the military departments using specified criteria, including that: (1) the original discharge was based on the policy of Don't Ask Don't Tell (as in effect before it was repealed pursuant to the Don't Ask, Don't Tell Repeal Act of 2010) or a similar earlier policy; and (2) the discharge characterization will be changed if, with respect to the original discharge, there were no aggravating circumstances that would have independently led to any discharge characterization except honorable. The bill prohibits "aggravating circumstances" from including: (1) an offense of sodomy committed by the member against a consenting person of the same sex; or (2) statements, consensual sexual conduct, or consensual acts relating to sexual orientation or identity, or the disclosure of such statements, conduct, or acts, that were prohibited at the time of discharge but that became permitted after such discharge. Each military department shall ensure that oral historians of the department: (1) review discharges between World War II and September 2011 based on sexual orientation, and (2) receive oral testimony of individuals who personally experienced discrimination and discharge because of actual or perceived sexual orientation so that such testimony may serve as an official record of such discriminatory policies and their impact on American lives. Specified military personnel records and discharge forms must be reissued in a manner that shall not reflect the sexual orientation of the member.