AIDS Awareness Act of 1987 - Requires the Attorney General to provide for confidential testing for exposure to the human immunodeficiency virus of any individual convicted of a Federal drug or sex offense if the offense occurred on or after January 1, 1978, and the conviction occurred on or after the effective date of this Act. Requires the cost of such testing to be paid by the individual and included in any court costs or fines ordered to be paid upon sentencing. Waives confidentiality for those convicted of rape who test positive. Requires the Attorney General to provide education and counseling, through existing prison medical facilities, to those testing positive.

Requires the Attorney General to make grants to States to pay for establishing State programs to test for such exposure in persons convicted of, or incarcerated in State penal institutions for, State drug or sex offenses if the State offense occurred on or after January 1, 1978, and conviction occurred after the effective date of this Act. Requires applications for grants to contain assurances of provision of education and counseling, through existing State penal institution medical facilities, for those testing positive.

Authorizes appropriations for FY 1988 through 1990.

Requires the Attorney General to study and report to the Congress regarding the viability of mandatory prison sentences for any person convicted of drug or sex offenses if such person was previously convicted for such an offense and tested positive for the virus.