Arizona Voluntary Grazing Permit Buyout Act of 2003 - Authorizes a permittee or lessee to waive to the Secretary of Agriculture, Secretary of the Interior, Secretary of Energy, or Secretary of Defense, as appropriate, a valid existing grazing permit or lease authorizing livestock grazing on Federal land in Arizona. Directs the Secretary concerned to cancel and permanently retire from grazing such waived allotments. Sets forth compensation provisions.