Rep. Toby Moffett (D-Conn.) is doing his bit to solve the summer jobs shortage. He's hiring 80 college students to go door to door begging alms for his Senate campaign.

Moffett's Republican rivals, incumbent Sen. Lowell P. Weicker Jr. and Prescott S. Bush Jr., are exceptionally well-heeled. Weicker is an heir to the Squibb fortune, and Bush comes from old money in steel and dry goods. They can spend as much of their own money as they choose, and each has raised $1 million. Moffett has $400,000 in his war chest.

If Weicker and Bush tire of dipping into their own funds, they can apply to Washington for handouts. As of April 1, the National Republican Senatorial Committee had amassed $26.4 million for its candidates. Moffett's hopes of outside help are not brilliant. The Democratic Senatorial Campaign Committee has raised $1.4 million.

Corporate America, which in 1980 spent $20 million to elect candidates, mostly Republicans, will be generous to Bush and Weicker, who are engaged in a bitter primary quarrel over which is the better Republican. Weicker, a member of the Armed Services Committee, has received bounty from various members of the military-industrial complex. Moffett, a former Nader raider who has engaged in high-profile tangle with Big Oil, the Pentagon and other large entities, is not down for a dime from the boardrooms.

In December, Moffett asked his two rivals to engage in negotiations to limit the size of their expenditures. Neither, understandably, was interested in either a ceiling or reduction.

Moffett's mendicants expect to knock on the doors of 150,000 Connecticut homes before they go back to college. In addition to putting the arm on householders, they will educate the voters on the issues and bring home the fact that money runs politics in a way not intended by the Founding Fathers.

One politician has tried the tin-cup approach this season. He is Tom Ryan Jr. who is trying to unseat Sen. John C. Danforth (R-Mo.) of the Ralston cereals millions. Ryan's experience in collecting $83 in an exhausting six-hour tour of St. Louis neighborhoods was not one to give hope to other Democrats suffering from a money gap.

The difference with Moffett is that after eight years of lively activism in the House, he has almost total name recognition and that the exercise is tightly structured and has already been field-tested. A team led by Sue Cadwell, an experienced door-to-door fund-raiser, did a trial heat in Hamden. Four canvassers, working in pairs, raised $60 in two hours.

Cadwell, who worked for Moffett's old consumer outfit, the Connecticut Citizens Action Group, is in charge of the canvassers, who were recruited from about 45 colleges throughout the state. The response was so large that Moffett headquarters had to call school employment offices to have the recruiting posters taken down. They have interviewed 150 people. Four Yalies made the grade.

Unlike the most famous student canvassers of the generation, the McCarthy volunteers of 1968, the new crop didn't even have to be asked to sacrifice beards or long hair for the cause.

"Nobody who came in was scraggly," Cadwell reports.

The recruits go through a week's training, a workshop, are chaperoned on their first outings and may not wear jeans or T-shirts.

They will be paid $135 a week and expected to raise $60 every time they go out between 5 p.m. and 9 p.m. If they fail to meet their quota, there is no danger that they will knock over a Good Humor truck or a 7-Eleven to take up the slack. In the event of a shortfall, they may be brought in for "retraining" or encouraged to take up other campaign duties.

"You are always successful at this if you are happy doing it," Cadwell says firmly. "The Connecticut Citizens Action Group raises its whole budget by door-to-door soliciting."

Once a week, the canvassers will be brought in for a quiz to ascertain that they are au courant with the congressman's stands.

The "rap at the door" was refined after the pilot outing in Hamden. The pioneers found that the best way to soften hearts was to come out and say, "Toby Moffett comes from a working-class family, and he's running against two millionaires from Greenwich."

"They don't want people doing a song-and-dance on their doorsteps," Cadwell says. "They want you to get to the point. They warm up when we say that good candidates often fail because of lack of money. We tell them we want small contributions from many people to counter contributions from the big interests."

Moffett expects his mendicants to raise $150,000, which could put his advertising spots on television for a week. But he'll be exploiting his disadvantage by calling attention to the scandal of American politics--that gaining election to the U.S. Senate is largely a matter of money.