Public broadcasting programs on radio and television may have a new twist early next year: paid advertising.

If the Senate accepts an amendment approved by the House last month, 10 public radio stations and 10 television stations around the country would be authorized, for the first time, to run advertisements.

The stations could carry up to four minutes of ads an hour, at the start or end of a program. Political or religious ads would be prohibited. The ads would be viewed only by a station's local audience. Neither WETA-TV nor WETA-FM is participating.

If his 18-month pilot program succeeds in bringing in extra money without corrupting the quality and character of public programming, all public stations across the country might be authorized to accept advertising as a way of replacing the federal dollars Congress and the Reagan administration are slashing from their budgets.

In the past, stations could display a corporate logo and note that a company had contributed money. But the firms could not buy ads to promote themselves or their products.

At issue, some say, is the freedom of public broadcasting to continue its subsidized search for, ad E. B. White put it, "the ideal of excellence, not the idea of acceptability." Critics argue that commercials will detract from the programs and may breed a dependency on advertising revenue that will keep stations from airing high-quality shows for which they can't find sponsors.

However, the broadcasters, while wary of advertising, are willing, for the most part, to try the experiment because they desperately need the money.

"We feel that any and all avenues that can raise funds should be tried out," said Thomas H. Otwell, spokesman for the Corporation for Public Broadcasting."

Public broadcasting has had a tumultuous history in this country since Congress founded the corporation in 1967 to funnel federal funds to the Public Broadcasting Service, the network of public television stations, and National Public Radio, the network of public radio stations.

The federal government now supplies about 25 percent of the support for public broadcasting, with the rest from states, corporations and viewers.

Appropriations were small at first: $5 million in fiscal 1969, $15 million the next year and still below $100 million in 1976. Born in a cozy delivery room during the Great Society years, public broadcasting had a frosty relationship under President Nixon, who accused broadcasters of airing biased, left-leaning programs and subsequently vetoed a two-year authorization bill for the corporation. He later agreed to a much smaller, single-year authorization bill.

Public broadcasting cruised along more comfortably under Presidents Ford and Carter, as appropriations rose to $162 million for the current fiscal year.

But President Reagan's austerity budget hacked away at public broadcasting, and Congress followed suit.Under the advance appropriations it has had for the past few years, the corporation was expecting $172 million for fiscal 1982 and 1983. But this spring, Congress cut the 1983 figure by 20 percent, to $137 million.

Under pending legislation, the House would cut the authorization for fiscal 1984 to $160 million and to $130 for the next two years. The Senate figures are even lower: $110 million for 1984 and $100 million for each of the next two years.

PETER M. Fannon, general manager of the National Association of Public Television Stations, a lobbying group, said that while the broadcasters welcome the opportunity to experiment, they fear that advertiser pressure might taint programming.

"That's a fear, not just of public broadcasters, but of anyone who has reviewed the history of broadcasting," he said.

WARD B. Chamberlin, president of WETA-TV and WETA-FM in Washington, said he has grave doubts about advertising on public stations. But "if it's successful, and doesn't seem to bring undue pressure on programming, then hell, I'm for it," he said.