FBI agents in Lakeland, Fla., arrested Joseph Paul Franklin late yesterday in connection with the August shooting of two black men as they jogged out of a Salt Lake City park with two white female acquaintances.

Agents said they also will question him about the shooting of Urban League President Vernon Jordan and as many as 22 other blacks who have been killed in highly publicized incidents in six other cities the past 15 months.

Franklin, 30, of Mobile, Ala., was arrested on a federal warrant charging him with violating the civil rights of the two dead Salt Lake City men. He was picked up as he prepared to give plasma at a blood bank in Lakeland, near Tampa. FBI agents had circulated his picture to blood banks in the area because they thought he often gave blood to make money as he traveled across the country.

Agents said Franklin is suspected of threatening the life of President Carter, and because Carter is scheduled to be in Florida Friday, Franklin's picture was sent to all area blood centers. The threat reportedly was contained in a letter to the president.

An employe of the SERA-TEC Biologicals plasma collection center recognized Franklin from his picture as he prepared to give plasma and called authorities. He was arrested without incident. FBI officials said he denied he was Franklin or that he was wanted for anything.

Franklin had been staying at the Lighthouse Gospel Mission in Tampa the past three days under the name of Barnum, according to the FBI. He was born James Clayton Vaughn Jr., but legalled changed his name to Franklin in Prince George's County, Md.

Franklin was last seen in Florence, Ky., near Cincinnati, where he was arrested and held a few hours late last month before managing an easy escape through a narrow crank-out window as officers conferred in a hallway.

Before that, he has been traced to Indianapolis in early April. It is Franklin's presence there that has led police to seek him for questioning in the Vernon Jordan shooting. Jordan was shot in the back May 29 with a 30.06 rifle in a motel parking lot.He was stepping out of the car of a white woman member of the local Urban League board when the sniper attack occurred.

Franklin has been reported to have been in Cincinnati in eary June about the same time two young black youngsters were shot as they walked to a store to buy soda pop.

Franklin has become the object of a nationwide manhunt in connection with the shootings, in part, because of antiblack statements he is reported to have made in Salt Lake City. Women who encountered him there have described to local police a man obsessive in his racial hatred and scorn. A desk clerk at one motel said Franklin had checked out, complaining that he had found the hairs of blacks in his bed. Later he bragged to a woman he picked up and took to another motel that he belonged to the Klu Klux Klan and had called blacks, according to testimony she gave to police.

Agents in Tampa cautioned last night at a press conference -- put off until the presidential debates had started -- that Franklin was wanted only in connection with the Utah shootings, and that they had filed no new charges against him.