Washington and baseball parted company 14 years ago, and ever since then the hopes of getting another team have risen every summer like the heat.

During lunchtime yesterday in downtown Washington, nearly 2,000 persons signed a 20-foot-long white banner supporting a new major league team here.

The top of the unusual petition, sponsored by the Connecticut Connection, a shopping and restaurant center above one of the city's subway stations, said in large red letters, "Connecticut Connection Supports Baseball in D.C., and So Does All of Washington." The banner-signing, which started Monday, has gathered more than 10,000 names.

"We need baseball in this city," said Dwight Deloatch, 34, of Northwest Washington, manager of a downtown print shop, as he added his name. "It keeps the kids off the streets, it brings revenue in, and the city loves it."

Washington's only brush with a local game comes during the annual Cracker Jack Old Timers Baseball Classic at RFK Stadium. The banner will be displayed at this year's game, which will be played July 1 before a national television audience.

Then in August it will be displayed at the Major League Baseball Owners meeting in Anaheim, Calif. Washington officials and residents are pinning their hopes on the owners voting at that meeting to expand the National League by two teams for the 1987 season.

As crowds gathered to sign the banner, two dozen youths, wearing red baseball caps, gave out blue and white buttons reading, "Baseball in '87," and they attracted other passers-by by chanting, "Help bring baseball to Washington. Sign up, sign up. It only takes a second."

The festive mood was enhanced by other young men and women who dispensed free hot dogs, popcorn, peanuts and boxes of Cracker Jacks. And in a corner stood a barbershop quartet in the traditional red and white jackets singing well-known baseball tunes.

A 40-foot helium-filled white balloon with red seams in the shape of a baseball floated above the scene, gently bouncing off the side of the red brick building.

The Washington Senators, who left town in 1971, were even represented. Dick Bosman, a pitcher with the Senators, looked at the huge baseball balloon and said laughingly, "Some people might say that I would have had trouble even hitting that one."

The banner, which will remain on display until tomorrow, has become so popular, organizers said, that they have lengthened it by two feet to accommodate more signatures.

John Hummer, 23, who recently moved to Washington from Detroit, said he signed "because if Washington gets an American League team, I'll get to see the Detroit Tigers."

Kevin Bacchi, 30, a chemical company manager from Annapolis, another signatory, said he hoped that "all the big corporations don't buy up all the tickets like they do for the Redskins," if baseball returns to the city.

"Washington loves baseball," said Judith Miller, president of the Connecticut Connection. "It's as American as apple pie, but better."