Dave Kenny, 18 and unemployed, recently noticed a poster of Uncle Sam in the window of a U.S. Army recruiting office here. "I want you," Uncle Sam was saying, so Kenny stepped inside.

A short time later, Kenny had become one of many persons discovering that Uncle Sam does not necessarily want, or need him. Long the last resort of the unemployed, the Army is being choosy these days.

"What am I going to do now?" Kenny asked Sgt. Al Castillo after being told that he had failed the Army's written exam and was ineligible to enlist.

"I can't get no job, I can't get no help," he grumbled. "But if I went out and robbed somebody, everyone would be involved."

Castillo shrugged his shoulders and smiled sympathetically at Kenny, a Cordozo High School graduate.

Nearby in the office, located at 5700 Georgia Ave NW, two recruiting officers were interviewing other young black men whose plights appeared much like that of Kenny. After months of seeking work, they had arrived at what they assumed was the last resort.

They were wrong.

For Kenny and Staples, the Army had closed ranks. Turned away like them are thousands of blacks who had thought that if all other job prospects fell through, Uncle Sam would come through.

According to Lt. Col. Jim Strachan, an Army information officer, there has been a steady increase in the number of persons rejected by the Army since 1972, the year the draft ended.

In the Washington area between October 1977 and July 1978, about 39 percent of those who tried to join the Army were rejected. In 1972, the figure was 27.6 percent, according to the Defense Manpower Center in Monterey , Calif.

Sgt. John May, a recruiter at the Georgia Avenue office, explained, "There seems to be this misconception that when you get into trouble you join the Army to get of town. No more. Now we require high school diplomas, brains, good health and clean record. Just like any good employer."

Meanwhile, the unemployment rate in Washington hovers at 9.7 percent, according to the city's Department of Manpower. For blacks between 16 and 19 years of age, the unemployment rate is a staggering 48.5 percent.

John Jacobs, president of the Washington Urban League, says the unemployment rate among black teenagers may be as high as 70 percent.

The number of blacks in the Army has increased by more than 50 percent since the draft ended in 1972. Blacks the comprised 15.3 percent of volunteers and, by late last year, that percentage had increased to 30 percent.

In recent months, however, a flood of high school graduates have volunteered for the Army and reenlistments have doubled, so the Army's manpower requirements have decreased, according to Army spokesman Dale Keller. "The need just isn't as great," he said.

About 20 persons visit the "Georgia Avenue office each week. "I guess we might take about two," Castillo said.

"Most of them have tried to find work, but they don't seem too fortunate," Sgt. Donna Montgomery said.

One day recently, Sgt. Castillo told three young men who had arrived at the office: "We have a film on jobs in the Army for you all today."

In the film, a black soldier says: "It pays good and I've learned a lot . . . in fact, it's been the best experience in my life," As the black soldier climbs back into a tank, a deep-voiced narrator adds: "Action. Critical responsibility. It can take you to Europe, San Francisco, Arizona . . ."

After the film, Louis Sedgewick, 17, a recent Cardozo graduate, said he had looked for work since June. "I'm just tired of people saying 'no'. But then, if I don't pass this test, it's back on the streets for me, he said.

Joseph Queen 19, who lives on Seventh Place NW, said he wanted to join the Army because his parents could not afford to send him to college.

"I've been out on the streets looking for work, but nothing comes through. All I learned in school was archery because I was hoping for a scholarship. But nothing came through. I need some recognition, something to get me going, so I figured the Army could help."

Later, Castillo informed each of the men that they had failed the written test. "You can come back and try again," he told them.

"We gonna have to do something," Queen replied.