America's Red Rock Wilderness Act of 2003

America's Red Rock Wilderness Act of 2003 - Designates specified lands in the following areas of Utah as components of the National Wilderness Preservation System: (1) Great Basin; (2) Zion and Mojave Desert; (3) the Grand Staircase and the Escalante Canyons; (4) Moab-LaSal Canyons; (5) Henry Mountains; (6) Glen Canyon; (7) San Juan-Anasazi; (8) Canyonlands Basin; (9) San Rafael Swell; and (10) Book Cliffs and Uinta Basin.

Sets forth administrative provisions regarding: (1) filing by the Secretary of the Interior of a map and a legal description of each designated wilderness area with appropriate congressional committees; (2) the exchange of State-owned lands within such areas; (3) Federal reservation of water rights; (4) measurement of setbacks for roads with wilderness; (5) authorized livestock grazing; and (6) withdrawal of such lands from disposition under certain public land laws.