Sen. Dennis Deconcini (D-Ariz.) asked the Justice Department yesterday to allow financier Robert L. Vesco to testify before a Senate subcommittee in Washington without fear of being arrested by federal authorities.

DeConcini made the request in a letter to Attorney General Benjamin R. Civiletti in which he said that Vesco had agreed "in principle" to testify before the subcommitte if "conditions for his appearance satisfactory both to the Justice Department and to Mr. Vesco" are established.

A Justice Department spokesman said DeConcini's request was received late yesterday and that there would be no immediate response.

Vesco is a fugitive from five federal indictments charging that he plundered a publicly held company of millions of dollars and then tried to buy his way out of trouble with a $200,000 contribution to the Richard Nixon election campaign in 1972. He fled to Costa Rica in 1973 and now lives in the Bahamas.

Vesco is now a central figure in a web of allegations that he also tried to buy influence in the Carter administration for the purpose of solving his legal problems. The charges were first made two years ago by columnist Jack Anderson, who alleged that Vesco had arranged for a group of Georgians to intercede on his behalf with White House aide Hamilton Jordan and presidential confidant Charles Kirbo.

Jordan and Kirbo denied the allegations and a grand jury investigation failed to substantiate the charges.

DeConcini's subcommitte on improvements in judicial machinery began looking into the matter after the grand jury foreman charged that there had been a "cover-up" during the investigation.