The U.S. Marine Corps, which celebrates its 205th birthday tomorrow, has taken the first step toward becoming a bigger outfit during the Reagan administration.

Commandant Robert H. Barrow has directed his staff to explore the possibility of beefing up support units so Marines would not have to go into battle as lean as they usually do.

This would mean recruiting more men and women. One big question is whether this could be done without sacrificing the current requirement that 75 percent of the recruits be high school graduates.

If this is deemed practical, the Corps is expected to seek approval of a gradual buildup over the next five years, spanning president-elect Reagan's first term. The starting point would by Oct. 1, 1981, the beginning of fiscal 1982.

Before Barrow directed his budget chiefs to allow for the possibility of an increase, the Corps was to consist of 188,100 Marines. Barrow also directed his staff to address the question of how many Marines should be added to provide men at the front with more backup.

Marine leaders said they feel civilian policy-makers only recently rediscovered how much the Corps could do to bring military power to bear in a hurry in a distant trouble spot. The Marines have recently been given starring roles in the North Atlantic Treaty Organization and in the quick-reaction force for the Persian Gulf.

The new idea is to let the Marines cover the north and south flanks of NATO and to be the spearhead, or at least a good part of it, for the Rapid Deployment Force being organized to respond to Persian Gulf emergencies. These roles contrast with the old image of the Marines as a Pacific force.

To the distress of many four-star Army and Air Force generals, the Carter administration went so far as to name a three-star Marine, Lt. Gen. P. X. Kelley, as commander of the Rapid Development Force. He commands only a planning staff in peacetime but, under the current setup, would become the field commander for as many as 200,000 troops called up from existing military outfits to fight as the Rapid Deployment Force.

Rather than replace Kelley or cut back the Marine Corps role in the Rapid Deployment force, a number of influential senators and representatives believe Kelley should get a fourth star to be an equal to the generals he works with as RDF commander.

There is also congressional sentiment for making the Rapid Deployment Force all-Marine rather than risk the confusion and command foulups that might come from trying to coordinate four different services in a Persian Gulf deployment. Sens. Gary Hart (D-Colo.) and Sam Nunn (D-Ga), members of the senate Armed Services Committee, and Rep. Jack Edwards of alabama, ranking Republican on the House Appropriations defense subcommittee, are among those who said they favor making the Marines the nation's RDF.

Nunn saad he will press for a committee probe of the RDF's command structure, adding that foulups during the unsuccessful hostage rescue attempt in April pointed up the dangers of fractured athority.