Bella Abzug, mired in a political losing streak, is trying to find an unlikely political home today - congresswoman for Manhattan's wealthy and powerful "Silk Stocking District."

It is Abzug's third campaign in 17 months, and after unsuccessfully setting her sights on the Senate an d City Hall she is aiming now to return to the house of representatives, which she abandoned in 1976 in search of the senate seat.

Abug, 57, and her little-known Republican opponent, S. William Green, have each made Abug the principal issue in this special election to fill the 18th district seat Edward I. Koch gave up when he became New York's Mayor.

Abzug stresses her six years of experience in Washington while Green describes Abzug as an abrasive, sometimes rude woman who will alienate the forces in Washinton whose support New York City needs for its financial survival.

Abzug's wide lead in recognition by New Yorkers and the fact that the East Side district is 3-to-1 Democratic should make her an easy winner, but the 48-year-old Green has outspent her and is clearly hoping that she will repeat the pattern of her Senate and mayoral failures.

In each of those campaigns she started with a lead and faded. Sen. Daniel Patrick Moynihan beat her by a nose in the September 1976 Democratic senatorial primary and she finished fourth in last September's mayoral primary.

The fact that this is a special election in which the turnout is expected to be extremely light and that the Weather Service is predicting new snow add to the uncertainties.

Abzug was first elected in 1970 after defeating Rep. Leonard Farbstein in Republican state legislature eliminatd her district and she ran against Rep. William F. Ryan in a primary. She lost, but Ryan died and Abzug was given the Democratic nomination and defeated Ryan's widow, who ran on the Liberal Party line.

"I always felt challenged by Congress," Abzug said as she shook hands along Lexinton Avenue yesterday. "I didn't leave because I didn't like it. I left to run for the Senate."

She wore one of her hallmarks, a broad-brimmed hat, but Azbug was low-key as she reminded people of the election and asked for their votes.

She may have been beaten twice and she may have a lot of enemies, but Abzug didn't have to introduce herself. The hat, the voice, the face and the broad frame moving slowly on feet she said were killing her from too many campaign walking tours triggered recognition in almost every passerby.

One of her enemies is a group called the Council for Community Consciousness, which is distributing pamphlets and working to defeat Abzug because of her advocacy of job rights for homosexuals and more widely available abortions, and her anti-Vietnam stand.

Green, a former assemblyman and former federal housing official, denies any connection to the anti-Abzug council.