The Supreme Court ruled yesterday that a public school system cannot refuse to renew the contract of an untenured teacher merely because he used his constitutional right of free speech to phone a radio station about a teacher-dress memo he didn't like.

But it ordered a lower court to take a second look at the case because it hadn't decided the first time around whether an Ohio school board would have rehired the teacher even if he hadn't made the phone call to a disc jockey.

The Mount Healthy school board hired the teacher, Fred Doyle, in 1966 and retained him under one- and two-year contracts.

The relationship was often tense. Doyle once got into an argument with another teacher who slapped him in an incident that culminated in a suspension of both and a walkout by a number of colleagues.

On other occasions, Justice William H. Rehnquist called in a unanimous opinion for the court, Doyle got into an argument with school cafeteria employees over the size of a serving of spaghetti, referred to students involved in a disciplinary complaint as "sons of bitches," and made an obscene gesture to two girls who failed to obey commands he gave as cafeteria supervisor.

Later, in February, 1971, the school principal circulated the school-dress memo. Doyle passed it on to a Cincinnati disc jockey who treated it as a news item. He subsequently apologized to the principal for not having first taken his criticism of the dress code through channels.

Citing the radio station episode, the board then refused to rehire Doyle, just as he was about to become tenured.

Doyle sued and won in U.S. District Court in Cincinnati. Judge Timothy S. Hogan ruled that the phone call - protected by the First Amendment - has played a "substantial part" in his dismissal, ordered him reinstated and awarded damages of $5,158. The Sixth U.S. Citcuit Court of Appeals affirmed.

Now the case is going back to the District Court. Doyle, meanwhile, is teaching in Miami Trace, Ohio.

In other action: FOOD STAMPS

In a unanimous ruling affecting only a few of the 18.5 million people who buy food stamps, the court held that the Food Stamps Act of 1964 allows the government to charge certain welfare recipients more than others.

The case involved Karen Hein, a divorced Muscatine, Iowa, woman who cares for her two children and who had been paying $46 a month for food stamps valued at $92.

After the State of Iowa provided her with $44 a month in transportation expenses so that she could attend a nurses' training school, the government raised the price of food stamps $12.

The court, in an opinion by Justice John Paul Stevens, said that the government was permitted by the food-stamp law to write regulations that took the transportation expenses into account in computing her income and the price she paid for stamps. LABOR

Upholding the National Labor Relations Board and the First U.S. Circuit Court of Appeals, the court ruled unanimously that a large, vertically integrated poultry enterprise must bargain with a union of truck drivers who deliver feed. The employer had contended that the drivers were "agricultural laborers" excluded from the National Labor Relations Act.