The U.S. military's touted new Rapid Deployment Force has come up for grabs in a behind-the-scenes battle that is expected to split the Joint Chiefs of Staff in a crucial meeting at the Pentagon today.

The question before the chiefs, who head the individual services as well as advise President Reagan on military issues, is which theater commander should control this new quick-reaction force that former president Carter organized to respond to trouble in distant spots like the Persian Gulf.

So much power, armament and policy ride on that question that Reagan, Defense Secretary Caspar W. Weinberger and Congress all are bound to become involved.The chiefs' expected split vote on the issue would automatically buck the issue to Weinberger, for openers. The law requires this on any issues dividing the chiefs.

The chiefs agree that they must find a new home for the RDF. The feuding between its operational commander, Marine Lt. Gen. P.X. Kelley, and his present theater commander, Army Gen. Volney F. Warner, has become so bitter that the whole future of the outfit is in jeopardy, the chiefs believe.

Warner heads the U.S. Readiness Command at MacDill Air Force Base in Tampa, Fla. He supervises Kelley and the RDF staff in peacetime. Kelley would command the outfit in wartime. Kelley would be empowered to draw on Army, Navy and Air Force units under current war plans. The idea of giving all this power to a general from the smallest service, the Marine Corps, has rankled many traditionalists in the other services, especially the Army.

Besides this feuding within the military, several members of Congress are sniping at the command and control structure of the RDF, an outfit with officers from all the services. Critics contend such fractured command would be disastrous in wartime. They cite as evidence the foul-ups on the Iranian rescue mission attempted by a split military command.

Give the Marines the whole RDF mission and let them call on other services for help, suggest some members of Congress, including Sen. Sam Nunn (D-Ga.) and Rep. Jack Edwards (R-Ala.), respectively members of the Senate Armed Services Committee and House Appropriations subcommittee on defense. Chairman John Tower (R-Tex.) of Senate Armed Services leans to this view and has promised formal hearings on the RDF.

While the chiefs agree that the RDF must be taken away from Warner of the Readiness Command, they are split on what other commander should get the new glamor outfit. Sources said Air Force Gen. David C. Jones, chairman of the Joint Chiefs, Gen. E.C. Meyer, Army chief of staff, and Adm. Thomas B. Hayward, chief of naval operations, all favor putting the RDF under the European command. Army Gen. Bernard W. Rogers, head of the European unit, then would supervise RDF war planning.

Although the Persian Gulf has been something of a no-man's land for the theater commanders until fairly recently, the European command is considered by most of the chiefs to have a legitimate claim on the area even though it mus concentrate mainly on preparing for land war in Europe.

But it is an open secret inside the Pentagon that Marine Corps Commandant Robert H. Barrow disagrees strongly with his fellow chiefs on this point and is prepared to split with them if the issue comes up for a formal vote today, as expected. Barrow has argued for putting the RDF under the Pacific command headed by Adm. Robert L. Long. Barrow has been telling associates that the Pacific command has the ships and know-how today for rushing Marines and other troops and their gear to the Persian Gulf.

Kelley himself, as RDF commander, has said the most straight-forward solution would be to establish a brand new command for the Persian Gulf, which would be home for the RDF. The chiefs apparently believe this would involve too much wheel-spinning.

Backers of Barrow's idea of putting the RDF under the Pacific command contend the quick reaction force could be kept as a Navy-Marine outfit for simplicity rather than remain the four-service conglomeration that has generated the skepticism in Congress.

Whichever theater command ends up with the RDF would stand at the head of the line in asking for new weaponry and other help. Carter administration Defense Secretary Harold Brown estimated that the Pentagon would spend $17.4 billion over the next five years beefing up the RDF. The RDF could consist of as many as 110,000 troops, with size depending on the crisis.