State Offices of Rural Health Act of 1989 - Amends title VII (Administration) of the Social Security Act to require the Director of the Office of Rural Health Policy to make matching grants to States to establish State Offices of Rural Health which shall: (1) coordinate their activities with the rural development activities of the Agricultural Extension Service; (2) make recommendations on improving the quality and cost-effectiveness of rural health care delivery; (3) report periodically to the Office of Rural Health Policy on their activities; (4) communicate and cooperate with five rural health research centers located in North Carolina, North Dakota, Washington, Wisconsin, and Arizona; and (5) provide rural health leadership and advocacy for rural residents. Specifies optional activities each State Office of Rural Health may undertake. Prohibits States from using more than 20 percent of their grant for research. Authorizes appropriations for such grant program from FY 1990 through 1992.

Requires an annual meeting between representatives of each State Office of Rural Health and representatives from the Office of Rural Health Policy to share information and coordinate strategies for improving the quality and effectiveness of rural health care delivery.