Rural Health Care Improvement Act of 1987 - Amends part A (General Provisions) of title XI of the Social Security Act to require that whenever the Secretary of Health and Human Services proposes a regulation or promulgates a final version of a regulation under titles XVIII (Medicare), XIX (Medicaid), or part B (Peer Review) of title XI of the Act which will have a substantial impact on small rural hospitals, the Secretary make a regulatory impact analysis available to the public.

Provides certain small sole community and rural hospitals with payment for extremely high cost cases (outlier payments) which represent five or six percent of the total payments made to such hospitals.

Sets aside ten percent of amounts expended by the Secretary on certain experiments and demonstration projects for projects relating exclusively to rural health issues.

Requires fiscal intermediaries to pay certain small rural hospitals for Medicare claims, at the latest, 30 days after receiving the request for such payment.

Amends title VII (Administration) of the Act to establish an Office of Rural Health Policy in the Office of the Administrator of the Health Care Financing Administration to: (1) advise the Administrator regarding the effects of changes in the Medicare and Medicaid programs on rural health; and (2) oversee compliance with provisions of this Act requiring regulatory impact analysis and rural health demonstration projects.