In one of those strange twists of politics, the Democratic Party's No. 1 glamour boy of 1982 is a paunchy, 82-year-old congressman with a bullfrog voice and a nose like a big red balloon.

"Claude Pepper is the sexiest man in America," Ann Lewis, political director of the Democratic National Committee, tells reporters. "We get more requests for him than for Robert Redford, Paul Newman and Warren Beatty combined. A visit by Claude Pepper is the biggest favor we can do for a Democratic candidate."

The reason is that Pepper, a Florida Democrat who chairs the House Select Committee on Aging, has come to symbolize the concerns of the elderly and what Democrats regard as one of the most potent issues of the election year: uneasiness over the Social Security system.

Pepper, who has campaigned in 22 states this fall, is a folk hero among a group of Americans that normally favors Republican candidates. In each of the last two presidential elections, 62 percent of Americans over 65 voted Republican.

GOP strategists are worried they may lose this edge Nov. 2. In a recent Washington Post-ABC poll, 62 percent of retired people interviewed said they intend to vote for Democratic congressional candidates this fall.

The politics of Social Security have a great deal to do with the shift. According to the same poll, 60 percent of the nation's likely voters disapprove of President Reagan's handling of the Social Security issue. Emotions are running high among older voters.

The older voter has come of age as a major political force in recent years. One American in five is 55 or older, and they register and vote in such high numbers that the Census Bureau estimates that one-third of the voters Tuesday will come from this group.

Both parties have spent millions courting these voters. And virtually every candidate in America has spent days meeting with groups of senior citizens.

Leaders of these groups have become major power brokers around the country. In Clearwater, Fla., for example, Marion T. Keith, 83, regularly delivers upward of 2,800 votes to Republican candidates from the retirement complex where she lives.

"The seniors are stirred up. They're angry. They voted for Ronald Reagan last time, but they're frightened about what he's going to do about Social Security," said Pepper, who has spent the fall hopping across the country from one senior citizen haven to another. "They're insisting that candidates pledge, 'I will not cut Social Security.' That's the word of art this fall: I will not cut Social Security."

Democrats seized on the Social Security issue almost from the day 18 months ago that the Reagan administration proposed, then backed down on, making major cuts in Social Security benefits.

The party has made television and radio ads (including one featuring Pepper); launched a "Campaign to Save Social Security;" prepared a 20-minute film for candidates to use before senior citizen groups, and sent out millions of letters in envelopes resembling those that contain Social Security checks.

Republicans countered with what some regard as the single most effective television ad of the year: one picturing a white-haired mailman delivering Social Security checks that contain an automatic 7.4 percent cost-of-living increase.

"I'm probably one of the most popular people in town," the mailman says in the commercial. "He Reagan promised that raise and he kept his promise inspite of the sticks-in-the-mud who tried to keep him from doing what we elected him to do . . . . For gosh sake, let's give the guy a chance."

The ad was so successful in its first run in early July that Republicans ran it again in August. They have now issued a second version of the commercial in which the postman says, "Well, I'm still delivering those Social Security checks."

This ad, according to Republican National chairman Richard Richards, is now running in areas with high concentrations of older people. Such appeals are not hard to target.

Half the Americans 65 and older live in the eight largest states, according to the House Select Committee on Aging. New York and California each has more than 2 million elderly residents; Florida, Pennsylvania, Texas, Illinois and Ohio each has more than 1 million.

Richards recently went to Florida, where 17.3 percent of the population is 65 or over, on a "truth trip" to attack the Democrats for their use of the Social Security issue.

"What we've done has been a defensive reaction. We were getting the hell kicked out of us," said Richards. "Our ads have blunted that. I think the Democrats were relying on their demagoguery on Social Security to really kill us. They've been running a campaign of fear."

Rep. Guy Vander Jagt (R-Mich.), chairman of the National Republican Congressional Committee, took this attack one step further in a fund-raising letter that accused Democrats of trying "to choke off our efforts to reform Social Security."

Democrats, he added, "drove Social Security to the edge of bankruptcy" by dipping into the system to fund their pet social welfare programs for people "who never paid a dime into the system."