President Carter's brother Billy registered as a foreign agent yesterday after a court order and revealed that he has received $220,000 in cash, almost $3,000 in gifts and almost $16,000 in travel expenses from Libya for work done during the past two years.

In his registration statement, Billy Carter described the $220,000 as installments on a $500,000 loan he waas promised by the Libyan government. Carter said he had requested the loan in return for his services.

There was no indication Carter would have to repay the loan, which Carter's registration statement said was agreed to without notes or anything in writing.

Carter registered as a foreign agent after being ordered to do so in an injunction handed down by U.S. District Court Judge John Garrett Penn.

When the president's brother filed the registration statement, the Justice Department said it would impose no penalties or fines against him even though he had refused to register as a foreign agent when asked to do so earlier this year by Justice.

A Justice Department spokesman said that one reason no action would be taken is that Carter had only recently received the cash payment from Libya for his activities. The registration statement says that Carter received $20,000 in January and another $200,000 in April of this year.

The spokesman also said that what Billy Carter had done for Libya "did not warrant criminal action." The spokesman pointed out that the last time anybody was even fined for failing to register as a foreign agent was 1963, when syndicated New York columnist Oleg Cassini was fined for not registering as an agent of Dominican Republic dictator Rafael Trujillo.

Besides the cash loans, gifts and travel expenses, the registration statement also said that Carter and a Plains, Ga., business associate identified as Henry R. Coleman had acted as go-betweens in trying to arrange an "increase in the allocations of crude oil that Charter Oil Co. of Jacksonville, Fla., is permitted to purchase" from Libya's National Oil Corp.

"No agreement has been reached in these discussions," the statement said. "Charter has advised Mr. Carter that it will pay him a commission should it receive an increase in its oil allocation from Libya."

A spokesman for the Washington law firm of Shea and Gardner, which represents the president's brother, said late yesterday he did not know what Charter Oil's Libyan allocation is but acknowledged it is in the "many thousands of barrels." Libyan oil is prized by East Coast importers because it is so low in sulfur.

Along with Carter's registration statement was an accompanying letter to the Justice Department from his lawyers stating that Carter is not now involved in any activities on behalf of Libya and has no activities "under consideration." Carter's lawyers said this did not mean he has "resigned" as an agent for Libya, but that no activities were under way.

Carter filed his registration statement after the Justice Department filed a formal complaint in U.S. District Court demanding that he register as a foreign agent or be held in contempt of court.

In registering, Carter in effect agreed to the order without admitting or denying any allegations in the complaint, such as the complaint that he "undertook specific activities calculated to promote Libyan foreign policy objectives" in the United States.

A spokesman for the president, who is vacationing on the Georgia coast, said the president would have no comment on his brother's filing as a foreign agent.

In Detroit, Sen. William Roth (R-Del.) called the disclosures "absolutely outrageous" and said he would seek a Senate investigation of Billy Carter's actions involving the Libyans.

Among the personal gifts Carter said he received from Libya were four god bracelets valued at $400, a saddle whose value exceeded $2,000, a serving platter worth $100, a ceremonial sword worth $50 and a suit of clothes estimated at $150.

Carter also said he and his associate Coleman were paid $15,980 in travel expenses for three trips they made to Libya, one in September 1978, a second in September 1979 and the third in December 1979.

Carter's links with the radical Libyan government of Col. Muammar Qaddafi have triggered criticism ever since he visited Tripoli in 1978 and then escorted Libyan officials on a visit to Atlanta later the same year. The president's brother accompanied as many as 10 Libyan officials he once described as "my best friends" on three separate trips to the United States, including receptions in New York and Washington in February 1979.

The registration statement also points out that Carter "arranged" for Libya's Ahmed Shahati to appear in February on the television program "Good Morning America" and another television show. Shahati is head of the Office of Foreign Liaison in the Libyan Embassy in Washington.

About the same time, Carter was heard making derisive remarks about Israel, which triggered severe criticism from American Jews.

"There's a hell of a lot more Arabians than there is Jews," Billy Carter said at one point. Then when he heard the criticism: "They can kiss my ass far as I'm concerned." CAPTION: Picture, BILLY CARTER . . . got $220,000 from Libya