Hurricane Rita Relief Act of 2006 - Amends the Internal Revenue Code to: (1) include Hurricane Rita employees (employees residing and working in the Rita GO Zone on September 23, 2005) as members of a targeted group for purposes of the work opportunity tax credit; (2) allow an additional tax exemption of $500 for providing housing to an individual displaced by Hurricane Rita; (3) exclude from the gross income of volunteer workers automobile mileage reimbursements related to Hurricane Rita relief work; (4) exclude from the gross income of individuals residing in a Hurricane Rita GO Zone certain cancellations of personal indebtedness; and (5) qualify residents in areas affected by Hurricane Rita for housing and education tax credits and other tax benefits currently available to hurricane victims in the Gulf Opportunity Zone.