Repeal Existing Policies that Encourage and Allow Legal HIV Discrimination Act of 2013 or the REPEAL HIV Discrimination Act of 2013 - Expresses the sense of Congress that federal and state laws, policies, and regulations regarding people living with HIV/AIDS should: (1) not place unique or additional burdens on such individuals solely as a result of their HIV status; and (2) demonstrate a public health-oriented, evidence-based, medically accurate, and contemporary understanding of HIV transmission, health implications, treatment, and the impact of punitive HIV-specific laws, policies, regulations, and judicial precedents and decisions on public health and on affected people, families, and communities.

Directs: (1) the Attorney General (AG), Secretary of Health and Human Services (HHS), and Secretary of Defense (DOD) to initiate a national review of federal (including military) and state laws, policies, regulations, and judicial precedents and decisions regarding criminal and related civil commitment cases involving people living with HIV/AIDS; and (2) the AG to transmit to Congress and make publicly available the results of such review with related recommendations.

Requires the AG and HHS Secretary to: (1) develop and publicly release guidance and best practice recommendations for states, and (2) establish an integrated monitoring and evaluation system to measure state progress.

Directs the AG and HHS and DOD Secretaries to transmit to the President and Congress any proposals necessary to implement adjustments to federal laws, policies, or regulations.

Prohibits this Act from being construed to discourage the prosecution of individuals who intentionally transmit or attempt to transmit HIV to another individual.