Defense Secretary Harold Brown has ordered his Pentagon deputies to seize on the rising unemployment rate as a way of filling the ranks of the military.

Brown set down his orders in a recent memo and followed up in person on Monday during a meeting of the Armed Forces Policy Council, a group of top civilian and military leaders at the Pentagon.

"Through growing unemployment figures represent a major problem," Brown wrote in his memo "they may act to improve our recruiting and retention."

He directed Robert B. Pirie, Pentagon manpower chief, and Thomas B. Ross, information director, to come up with "a vigorous effort" in this regard.

He called on those deputies to make sure "no one leaves active duty without knowing full well the current state of the overall job market."

Also, continued Brown in his memo, a Pentagon recruting drive geared to the realities of the recession should assure "former service members who are now seeing the vagaries of the civil sector that they are welcome on active duty."

The national experiment in an all-volunteer military has been jeopardized by lack of enough volunteers in the past. The bigger problem right now, however, is persuading skilled people already recruited to remain in the service.

Already, the Navy has had to tie up one ship at a Norfolk pier for want of enough petty officers. The Navy is currently scrambling to fill the billets on the aircraft carrier John F. Kennedy so she can return to the Mediterranean next month.

As military leaders see it, Brown's idea of signing up more recruits from among job-hungry youths does not address this key problem of stemming the exodus of skilled people. Those specialists are sought by industry, even during the current recession.

However, military leaders do acknowledge that exploiting the recession would make it easier to sign up beginners for the armed services, perhaps ones of higher quality than have been volunteering recently.

The bleak job market is already driving an increased number of young people to the recruiting stations, according to Pentagon figures.

In April, the Army hoped to sign up 8,500 men and women and got 10,000, or 124 percent of quota. By contrast, the Army was 1 percent under its quota for the six-month period ending in March 1980.

The Navy and Air Force also did well in April, each reaching 102 percent of quota.

Only the Marine Corps continued to fall short, recruiting 96 percent of the total sought in May. This was up from 89 percent in the previous six-month period, however.

One reason the corps is having a harder time filling its ranks than the Army is the higher entrance standards, including the requirement that 75 percent of the volunteers have high school diplomas. The recession eventually could help the Marines, too.

Youth unemployment is indeed rising, according to Labor Department statistics.

In May 1979, 14.2 percent of the men and women aged 16 to 19 were jobless. By this May, the percentage had climbed to 17.4 percent, according to the Labor Department's figures.

Black youths have found the going particularly rough, both this year and last. Unemployment among black men and women aged 16 to 19 was 36.1 percent last May and 35.2 percent in May 1980.

The upward trend also showed up in the unemployment rates for people aged 20 to 24, prime objectives for military recruiters.

The jobless rate among men and women in this age bracket jumped from 8.9 percent to 12.7 percent between May 1979 and 1980, according to the Labor Department.

Brown in his memo to man power chief Piere and spokesman Ross said he wanted Ross to "take the lead in orchestrating the vigorous and external campaign" to inform people already in the service and those who might want to return to uniform about the nation's bleak employment picture.