Frank Sinatra was in town last night. His friend, the president of the United States, stopped by to say hello.

"Well . . . let me apologize for not being dressed for the occasion," joked President Ronald Reagan to the black-tie crowd at the third annual Ambassadors' Ball, "but the way this day has been going, I would have had to get dressed this morning for the event."

This was the president's first time back to the Washington Hilton Hotel since the assassination attempt there last March and he appeared to be in high spirits, making an evening of party rounds with the first lady.

A special sharpshooter team rode near his limousine en route from the White House. The president's car was driven into the heavily guarded hotel garage -- without the usual group of reporters around to watch his entrance. He left the same way. But he didn't mention the shooting.

He did talk about his favorite topic of late, the budget.

"Everyone is paying so much attention to the budget these days. I don't know why, it happens every year," he kidded, to much laughter, while making a pitch for more private contributions to public charities.

Last night's ball was expected to raise $250,000 for the National Mutiple Sclerosis Society, of which Sinatra is the national fund-raising campaign chairman. Sinatra was almost as well protected as the president. But he got more laughs.

"The last time I saw so much power in one place was when I stopped to fill up my car at Billy Carter's gas station," Sinatra opened. Medium laughter.

"It's good to see my neighbor from Palm Springs, Lenore Annenberg, here tonight," Sinatra said of the chief of protocol. "I'm so happy she found work. You're a credit to your country, Lenore, and I'd curtsy for you anytime, no matter what the hell the occasion is." Loud laughter.

"I'm very happy to be here," concluded Sinatra. He didn't move from the dais all night. But then again, it was sort of hard to move anywhere. It was a very big ball.

Charity balls seem to be in these days. This one was underwritten by 27 corporations, including Occidental Petroleum, Dow Chemical and Norton Simon, all of which bought tables for lots of money. How much you paid however, did not seem to be in direct correlation to how close you got to sit to the dais and stare at Frank and Barbara Sinatra. The politicians were very close. The second ring seemed to be the corporate tables.

But everyone ate the same food: roast beef, sauteed vegetables and baked Alaska.

Eleven hundred guests--members of the diplomatic corps, the administration and social Washington -- careened in the ballroom, some sporting diamonds the size of Ping-Pong balls, hair styles even last night's thundershowers could not budge, and dresses that were high-waisted, low-waisted and very low-cut.

"My husband said I looked too big in this dress," said the wife of a Cabinet member, eyeing her chest.

"No," corrected the secretary, "I just said that I could see more than usual."

That was "not for attribution."

Security was very tight, and all the guests were required to file through the one metal detector set up at the ballroom doors. Every other woman set it off. Metallics are a big fashion this year.

As a security precaution, the hundreds of rainbow-colored balloons that festooned the Hilton lobby were not allowed in the ballroom. "The Secret Service told me last night at 6 that I could have the balloons or the president," said Ursula Meese, wife of presidential counselor Edwin, and chairwoman of the event, "so I took the president."

Once inside, Republican public relations man Robert Keith Gray -- who orchestrated this event and many others like it since last January -- had a hard time getting the crowd under control. This was a table-hopping group.

"No one wants to sit down," one woman called to Secretary of Defense Caspar Weinberger.

"I guess this is just an unruly crowd," said Weinberger.

"Very unruly, these Republicans," said the woman. Among the other Republicans were Labor Secretary Ray Donovan, Transportation Secretary Drew Lewis, Treasury Secretary Donald Regan, national security adviser Richard V. Allen and presidential spokesman Larry Speakes; a few Democrats, including Majority Leader Jim Wright of Texas; and the ambassadors of about 60 countries.