The Army is playing a numbers game to cover up the fact that it is recruiting fewer than half of the reservists it needs, the General Accounting Office said yesterday.

Instead of owning up to the big gap, the GAO complained in the latest of a series of military manpower reports, the Army keeps lowering its reserve goals to match the number of people its recruiters believe they can sign up.

The result, said Congress' investigative agency, is the projection of "a false image of the actual recruiting situation" to Congress and the Defense Department.

Zeroing in on what it regards as the right and wrong numbers, the GAO said the Army told Congress it had reached 92.5 percent of its recruiting objective in fiscal 1978 when the service really got 48.4 percent of the number of reservists needed to carry out existing war plans.

The Army National Guard is playing the same kind of numbers game, GAO said.

The watchdog agency also critized Pentagon civilian leaders for failing to fulfill promises to Congress to "set recruiting objectives based on manpower needs," not on how many people could be induced to join a reserve unit in a given year.

Instead of tolerating the continued veiling of the problem's true dimensions, said GAO, "the nation may have to consider" rewriting war plans to give a lesser role to the reserve or drafting people to fill the vacancies.

Gen. Bernard W. Rogers said earlier this year when he was Army chief of staff that conscription may be the only way to fill the reserves. Army Secretary Clifford L. Alexander disagreed, contending that the draft will not be necessary.

The Carter administration, in responding to GAO's complaints that the Army is failing to compare recruiting results with actual defense needs, said the present goals for the reserves represent "a realistic glidepath towards achievement."

David Sitrin of the Office of Management and Budget added in the administration's letter of rebuttal that "under current circumstances" the "glidepath" approach is "prudent."

The switch from the draft to the all-volunteer military in 1973 caused today's big shortages in the reserves. Once draft calls stopped, young men no longer joined to avoid conscription. Also, reserve units are running out of the Vietnam-era servicemen obligated to serve in them. And recruiting new people or veterans for the reserves has proved tough.

The GAO said that given the smaller pool of young people available in 1980s, signing up new recruits for reserve units is likely to become even more difficult.

The nation's war strategy at present is to depend heavily on reserve forces to back up the active-duty combat troops in the early days of a war. But this strategy is in jeopardy, GAO said, because the reserve force standing behind the active Army, Navy, Air Force and Marine Corps are 200,000 people short.

The Army is in the worst shape in its reserves, GAO said, with a shortage of 146,000 people, mostly in the key combat jobs.

Other problems in the reserves, GAO said, include many people holding jobs they are not qualified to perform and the exodus of experienced persons.