Renovate and Enhance Veterans' Meeting Halls and Posts Act of 2013 or REVAMP Act of 2013 - Amends the Housing and Community Development Act of 1974 to require the Secretary of Housing and Urban Development (HUD) to make grants, on a competitive basis, to eligible veterans service organizations for repairs and rehabilitation of their existing facilities.
Defines "eligible veterans service organization" as: (1) a tax-exempt entity organized on a local or area basis; and (2) a local or area chapter, post, or other unit of a national, regional, statewide, or other larger entity of which local or area chapters, posts, or units are members (but not any such national, regional, statewide, or other larger entity itself).
Prohibits an eligible veterans service organization from receiving such grant amounts, for any single fiscal year, in an amount exceeding the lesser of the cost of the proposed repair or rehabilitation or $200,000.
Makes a grant recipient ineligible to receive another such grant until after five succeeding fiscal years.
Prohibits the use of such grants for construction or acquisition of a new facility.