While bankers and retailers have warily eyed the advent of smart cards -- microcomputers encased in credit card-size plastic -- one small company has found a way to sell the technology to the health care market.

A smart card is, in essence, a memory card containing a silicon chip and integrated circuitry similar to the chip and circuitry in a personal computer. It has nonerasable memory able to store eight times the data of conventional magneticstripe cards. The cards hold great promise as a way of reducing the cost of financial transactions, particularly the processing of checks, and as a way of combating the fraud and counterfeiting that currently plague charge, credit, and magnetic-stripe cards. But although the smart card is currently used by banks and retailers in Western Europe, their counterparts in the United States have been content merely to study it.

In the meantime, Amrix Corp., a small Houston start-up, has proven that there is lots of opportunity for companies that play their cards smart. Amrix is selling a version of the cards to hospitals that facilitates quick and accurate billing of patients. The cards can also be programmed to accept patients' medical data, such as blood types and allergies.

In May, Amrix began delivering its smart card-based charge tracking system to the first of 10 hospitals that have ordered it. Amrix, founded in October 1982, doesn't own the smart card patent and must import its cards from Bull of France, a patent holder and trading partner with Honeywell Inc. Amerix buys the basic version of the card, then adds its own programs and modifications.

William Morgan, president of Amrix, expects his company to rack up at least $4 million in sales in the next year. "We're anticipating widespread acceptance of the product in the United States," he says. "I conservatively estimate the domestic market for [the cards] to grow by at least 25% a year for the next few years."

Honeywell introduced smart cards to the U.S. market at the 1982 National Computer Conference. Only three French companies and one American concern, SmartCard International Inc. in New York City, are authorized to use the original patent. SmartCard is studying several uses for the card, but no tangible results are expected in the near future. "Don't expect any products from us this year," says Arlen Lessin, president of SmartCard.