Smokeless Tobacco Control Act of 1985 - Directs the Secretary of Health and Human Services (Secretary) to develop educational programs and materials and public service announcements respecting the dangers to human health from the use of smokeless tobacco, and to make such programs, materials, and announcements available to States, local governments, and school systems. Requires the Secretary to report annually to the Congress on the activities undertaken in this regard.

Permits the Secretary to make grants to States to assist in the development of educational programs and materials and public service announcements respecting the dangers to human health from the use of smokeless tobacco, to assist in the distribution of such programs and materials, and to assure that individuals will be able to make a mature judgment respecting the use of smokeless tobacco, and to establish a minimum age for the purchase of smokeless tobacco.

Defines smokeless tobacco.

Amends the Internal Revenue Code to disallow the deduction for expenses incurred in advertising smokeless tobacco.

Imposes an excise tax of 32 cents an ounce (or fraction thereof) on smokeless tobacco.

Establishes within the Treasury the Cancer Research and Smokeless Tobacco Education Trust Fund. Transfers amounts received from the smokeless tobacco excise tax to the trust fund. Provides that amounts from the trust fund shall be used to fund grants to the States to develop programs and for cancer research by the National Institutes of Health with emphasis on the relationship between smokeless tobacco and oral and other forms of cancer.