Health Care for the Homeless Act of 1987 - Directs the Secretary of Health and Human Services to make grants to qualified entities to enable them to deliver outpatient health care and outpatient mental health, case management, and advocacy services to homeless individuals. Requires such entities to be qualified recipients of State Medicaid payments.

Assigns preference to grant applicants with experience in delivering health care or mental health services to the homeless, medically underserved populations, or individuals who are chronically mentally ill. Requires services under such grant to be provided 24 hours a day. Sets forth other grant requirements.

Provides certain limitations on charges for services. States that services must be provided regardless of the recipient's ability to pay. Sets forth restrictions on the use of grant funds.

Limits any such grant to 75 percent of the cost of services. Outlines application requirements and procedures.

Authorizes appropriations for FY 1988 through 1990.

Amends the Social Security Act to provide that clinics may provide Medicaid services to the homeless.