The United States should reinstitute the draft to fill the projected need for 150,000 extra troops in Europe after 90 days of fighting, Gen. Bernard W. Rogers, North Atlantic Treaty Organization commander, told the Senate Armed Services Committee yesterday.

"We're going to be short a minimum of 150,000 infantry, armor, artillery, combat medics" 90 days after a war starts in Europe, said Rogers, who wears the two hats of commander of U.S. and of allied forces in Europe. He has advocated the draft in the past on philosophical grounds. Yesterday, however, he tied it to the specific requirement of reinforcing Europe.

Rather than pay bonuses to the combat troops already serving in the volunteer Army or extending their obligated service from six to eight years, "the answer is to have a draft for that purpose," Rogers said.

Under Rogers' recommendation, young men would be vulnerable to a draft lottery for one year. Those called would be trained in a crucially needed combat skill for four months and then be released to pursue civilian careers unless war broke out.

"Let's face it," Rogers said, declaring that his idea has no chance of becoming reality, "unless each of the Joint Chiefs of Staff sit in front of you and say we must have it and the administration is going to support it, why, 'Old Bernie' Rogers is just whistling in the dark."

"Well, I'm whistling with you," responded Sen. Sam Nunn (D-Ga.), saying that he, too, favors reviving the conscription that was discontinued in 1973 at the end of U.S. involvement in Vietnam. Sen. Gary Hart (D-Colo.), another member of the Armed Services Committee, this week introduced a bill to establish a commission to the study the feasibility of requiring 18-year-olds to perform some form of national service, with the military being an option.

The NATO commander, assessing allied forces, said they were growing stronger but still could not stop an invasion of Western Europe by the Warsaw Pact nations. The United States could not get 10 divisions to Europe in 10 days as required by the war plans, Rogers said, and would have to decide "fairly quickly" whether to resort to nuclear weapons.

He pleaded with Nunn not to reintroduce last year's amendment calling on the Reagan administration to withdraw U.S. troops from Europe to protest U.S. allies' failure to live up to their promises to build support facilities, such as airplane shelters. Nunn, whose amendment lost narrowly, did not reveal his plans for this year.

Rogers complained that he is short of the people he needs to run the new weaponry being sent to Europe, such as the ground-based cruise missiles manned by the Air Force. The current ceiling on U.S. forces in Europe, backed by the Reagan administration and protested by Rogers during last year's budget process, is 326,400 troops.

"I need 10,000 more spaces, primarily for the Air Force," Rogers said. Because of the ceiling, he said, he confronts the choice of sending experienced people home or holding off on the delivery of new weapons and their support personnel.

Asked if he was protesting President Reagan's defense budget request for fiscal 1986, which includes the 326,400-person ceiling, Rogers replied that he was requesting that manpower cuts be made by limiting each service to a total number of personnel rather than by imposing reductions on a specific theater, such as Western Europe.

"The basic challenge to NATO," Rogers said, "is to convince people that there is a threat to their freedom." He said that if NATO nations do not do more for their own defense, the Warsaw Pact could begin to look so powerful that European leaders might decide to give up rather than fight.

Committee Chairman Barry Goldwater (R-Ariz.) agreed and said he would press Reagan to release top-secret photographs documenting the Soviet buildup. Goldwater said that for 25 years U.S. intelligence officials have resisted releasing pictures taken by satellite for fear that they would reveal to the Soviets the extent of U.S. surveillance capabilities.

"If the Russians haven't figured that out by now," said Goldwater, "then they're not as smart as I think they are."

Rogers supported releasing secret photos, saying that pictures of the fuel lines the Warsaw Pact is laying from east to west for its military forces would be among those that would help build public support in Europe for higher defense spending.