The D.C. school system may open the city's first full-time public school health and birth control clinic at Anacostia High School, where youths will be able to obtain birth control pills and other contraceptives, if parents approve the idea at a public hearing tomorrow.

Despite vehement opposition from those who say that such clinics would encourage sexual activity among teen-agers, facilities have been established in 35 schools across the country.

Mayor Marion Barry's blue ribbon panel on teen-age pregnancy has suggested to D.C. Superintendent Floretta D. McKenzie that birth control clinics be established in District schools. McKenzie has indicated support for the idea, but has asked for a public hearing to get parental reaction.

McKenzie will make her final recommendation to the Board of Education's Committee on Student Services and Community Involvement, according to a committee spokesman, and the board probably will vote on the proposal in January. If approved, the clinic could be in operation by spring.

The clinic would be similar to a program in St. Paul, Minn., where pregnancy rates among high school students dropped 64 percent in the first three years. The number of teen-age mothers in the District has reached reached nearly 2,000 annually, a fifth of the city's births.

Planned Parenthood officials and Anacostia Principal Walton Breckenridge will present to parents at tomorrow's hearing a proposal for the clinic, which also would provide, for free or a minimal charge, health services such as physical examinations, blood pressure tests, immunization and drug counseling.

Planned Parenthood would operate the clinic and a primary goal would be to reduce the birth rate among teen-agers. "No one has come up with anything that works better," said Breckenridge. "I just think an ounce of prevention is worth a pound of cure."

Breckenridge said that if parents decide in favor of the clinic, they also will determine whether birth control devices will be distributed at the school or at a nearby Planned Parenthood clinic and whether parental consent will be necessary for students to obtain such devices, he said.

"The clinic will not offer abortion counseling, but will give pregnancy tests," explained Sharon Robinson, special projects coordinator for Planned Parenthood in the Washington area.

The effort to open a clinic in the District stems from a nationwide movement that began in several midwestern cities in the mid-1970s.

The clinics have been established by various private groups and funded by a mixture of public and private funds. Most have been set up in schools serving low-income, usually predominantly black neighborhoods where teen-age pregnancy rates are generally highest.

Locally, there was a birth control clinic at H.D. Woodson Senior High School, Fifth and Eads streets NE, from 1975 to 1980, according to Robinson.

The clinic was phased out, she said, because it was not a comprehensive health clinic, it provided only part-time counseling and it operated at a time when teen-age pregnancy was not as widespread.

Anacostia High School was chosen as the proposed site of the first District clinic because of the principal's enthusiasm "and because Anacostia students are underserviced in terms of general medical care and access to family planning services," Robinson said.

"Also, Anacostia is near a Planned Parenthood facility, so if parents decide contraceptives can't be distributed in school, kids can be referred to a nearby facility," she said.