Rep. John W. Jenrette Jr. (D-S.C.) yesterday became the third House member indicted in the FBI's Abscam undercover investigation when a federal grand jury here charged him with bribery and conspiracy.

The indictment, which comes less than two weeks before Jenrette must face voters in a primary runoff election, alleges that the congressman and codefendant John R. Stowe of Richmond conspired to receive payoffs in return for a promise to introduce a private immigration bill for the "client" of an undercover FBI agent.

On Dec. 6, according to the indictment, Jenrette called the agent to say that Stowe would pick up $50,000 to "insulate" the congressman from receiving the cash.

A short time later, the congressman called the FBI agent to say he had received "the package" and to ask for the name and country of the foreign businessman, the charges said.

On Jan. 7, the indictment continued, Jenrette and Stowe met with the undercover agent, Anthony Amoroso, and an FBI informant, Mel Weinberg, and Jenrette "proposed that he would contact Sen. Strom Thurmond" to seek his assistance in introducing a similar bill in the Senate. Thurmond (R-S.C.) was never contacted, the grand jury said.

Jenrette has acknowledged receiving $10,000 from Stowe after meeting two men to discuss what he described as a business opportunity in his district. In an $11 million civil suit filed against the government earlier this week, Jenrette claimed that he was drunk when he met with FBI operatives and was entrapped.

In a statement issued in Florence, S.C., yestereday, Jenrette said he was "relieved" that formal action had been brought against him after months of news leaks and years of investigation.

But he said the return of the indictment "in the late hours of this campaign" only gives "credibility to my contention . . . that the Justice Department is dedicated to destroying me." He estimated the cost of its efforts to do so over the years to be "in the millions of dollars."

He said that department officials are trying "to accomplish at the ballot box what they have failed to do over the last five years at the jury box."

Jenrette's attorney, Kenneth Michael Robinson, said yesterday that the indictment was expected, but he was critical that it came just before Jenrette faces a runoff election. "I'm a bit baffled," he said. "It seems to me these charges could have been brought a month ago."

Reps. Michael O. (Ozzie) Myers and Raymond F. Lederer, both Democrats from Philadelphia, already have been indicted in connection with the Abscam investigation. A federal grand jury in Brooklyn is expeced to be nearing a decision on whether to issue similar indictments against two House committee chairmen, Frank Thompson (D-N.J.) and John M. Murhphy (D-N.Y.).

The Jenrette indictment contains more detail than did those against Myers and Lederer, who were indicted for bribery and racketeering. Though none of the indictments mentions it, news reports of the Abscam investigation in early February said that the FBI used a hidden videotape camera to record transactions between members of Congress and undercover operatives posing as representatives of Arab businessmen.

The conspiracy charge against Jenrette and Stowe details several calls from the congressman to the undercover agents -- calls that apparently were recorded.

According to the indictment, Jenrette and Stowe first met with Amoroso and Weinberg in Washington on Dec. 4 and discussed a $100,000 payoff for the immigration bill. The next day, Jenrette allegedly made the arrangement to have the first $50,000 picked up.

On Jan. 28, according to the indictment, Jenrette told the undercover agent that he would "cause" Thurmond to introduce an immigration bill in the Senate for an additional $125,000.

Jenrette got the most votes in his primary election last Thursday, but received less than a majority, so he was forced into a June 24 runoff against state Sen. Hicks Harwell.

Jenrette has been investigated by a grand jury in South Carolina over the last few years and was hospitalized for six weeks this spring for alcoholism treatments.