Rural Veterans Care Act of 2006 - Establishes the Assistant Secretary for Rural Affairs in the Department of Veterans Affairs to: (1) formulate and implement all Department policies and procedures that affect veterans living in rural areas; (2) carry out demonstration projects to examine alternatives for expanding veterans' care in rural areas; (3) reevaluate, and revise as necessary, Department guidance and procedures related to the use of fee basis care nationwide; and (4) establish and operate at least one and up to five centers of excellence for rural health research, education, and clinical activities.

Directs the Secretary to conduct a pilot program for improving the access of veterans who reside in highly rural or geographically remote areas to certain health care services.