The Republican Party, which has watched a Democratic president preempt such traditional GOP goals as cutting red tape and balancing the budget, is honing a new campaign issue that has been a Democratic preserve in recent years: corruption in government.

The specific case of "corruption" that Republicans are talking about across the country is the Korean influence-buying scandal, which many GOP officials see as a heaven-sent political opportunity for the party.

"It's tailor-made of us." says an enthusiatic Guy Vander Jagt (R-Minch.), chairman of the Republican congressional campaign committee.

"It's a high, hard one right over the center of the plate," Vander Jagt continues. "We ought to be able to hit it for a homer."

"Koreagate" first emerged as a political issue this spring, when junior Republicans in Congress started talking about the affair on visits home.

The young GOP members received an encouraging response, several of them say, and came back to Congress urging senior Republicans to work Korea into their speeches. The older party members demurred at first; they wanted to avoid the whole subject of Korea, because it sometimes involved friends and long-time leagues.

Recently, though, some of the nation's leading Republicans in and out of Congress have been bringing up the Korean affair on the hustings.

John Connally, senior spokeman for the party's southernwest wing is telling audiences that Congress' Korea investigation - being run by the House Democratic leadership - could be the biggest cover-up in the history of the nation."

Bill Brock, the party's national chairman, has also lambasted the Democrats for the sluggish pace of the investigation. House Minority Whip Robert Michael (R-III.) suggested last week that the Democrats have been "foot-dragging" to protect fellow party members.

Some Republicans have resisted Rep. Millicent Fenwick (R.N.J.), a member of the HOuse committee investigating the scandal, says it would be "a political fortune in the matter.

House Minority Leader John Rhodes (R.Ariz.) also plays down the political impact of the Korean affair, saying he is getting "very little" mail on the subject.

Rhodes did join with Senate Minority Leader Howard Baker (R. Tenn.), though, in demanding that President Carter appoint a special prosecutor in the Korean scandal.

That request seemed to anger Carter. The President forcefully rejected it last week. But Rhodes & Baker indicated they would not let the proposal drop.

Other congressional Republicans have been peppering Carter's attorney general, Griffin B. Bell, to move faster on his Korean investigation - with a press release accompanying each new demand.

Rep. Chalmers Wylie (R-Ohio) is coming at bell from a different side. He has introduced a resolution demanding that Justice turn over all of its Korean records to the House.

The measure, which Wylie may force to a vote this week, would amount to a congressional vote of confidence on Bell's work. That would embarrass some Democrats, who have joined Republicans in asking for faster Justice Department action - or a separate, independent investigation.

Vander Jagt and other campaign committee members have been urging their House colleagues to remind the voters of the Korean affair and of the Democrats' problems in probing it. That recommendation has been widely accepted.

In Southern California, according to Rep. Robert Dorman, a Republican from Santa Monica, "this scandal is becoming the No. 1 issue. Even when I don't bring it up, people ask me about it."

In Southern Pennsylvania, Robert Walker (R-Pa.) says, the political impact of "Koreagate" is unmistakeable. "People know this is Congress."

In Iowa Rep. Jim Leach. a fresh-affair, and thus magnified its poten.

"To the extent this whole mess sickens people and makes them dissatisfied with the Congress," Vauder

In Iowa, Rtp. Jim Leach, a freshman Republican from Davenpot, was aske dto speak briefly last spring at a fund-raiser that featured leading Midwestern Republicans.

Leach used the occasion to critize the Democrats' Korea investigation and ended up stealing most of the headlines and attention from his more prominent colleagues. Since then Iowa Republicans have regularly invoked the Korea scandal at political functions.

The angry resignation of chief investigator Philip A. Lacovara caused a quantum leap in public interest in the affair, and thus magnified its potential political impact.

Precisely what that impact will be is unclear. Republican leaders suggest tha it is not like to affect any particular elections. Instead, they hope it will enchance their party's general image in the 1978 congressional races says. "it goes along beautifully with our basic massage - the Congress is overdue for a change."

Many House Democrats - particularly junior members whos political fortunes are uncertain - unhappily agree that the scandal and questions about the investigation will aid the GOP.

"I can't believe we could do this to ourselves," says Rep. Peter Kostmayer, a freshman Democrat from subsurban Philadelphia. "What conclusion will people draw about our party when they read about this comedy of errors?"

House Speaker Thomas P. (Tip) O'Neill (D-Mass.) received that message is spades last week during a series of meetings with concerned first and second term House Democrats.

"I ran on a plat form of "integrity" and I won by 1,300 votes," one freshman complained to O'Neill. "If I tried that today, the Republicans would cream me."

Several junior Democrats have joined Republicans in critizing the House leadership for the halting nature of the investigation. That has its rewards. Kostmayer was applaused editorially to two Philadelphia newspapers this week for his fortnight demand for a more speedy investigation.

Although the Republicans are uniformly demanding a quick and complete investigation, they say privately that the longer the probe drags on, the better a political issue it will become.

Since newly named chief investigator Leon Jaworski does not plan to come to Washington until mid-August, it seems unlikely that the committee can proceed to public hearings before winter. That means a final wrap-up of the probe will probably not come before the middle of next year when congressional campaigns are underway.

Whatever the effect of the scandal on actual campaigns, Republicans are already comvinced that it will help neutralize the memories of Watergate that still taint the GOP.

"There are still people who think of us as the party of Watergate and cover-up," says Leach ruefully. "Now we can show them that it is our party that's anxious ot investigate corruption in government."