A Pershing II rocket motor was fired successfully at dawn Tuesday, sending a plume of exhaust across the plains in a pollution test designed to help determine whether the site can be used to demolish the missiles as required by a new U.S.-Soviet treaty.

Originally scheduled for May 20, the test burn had been delayed again and again because of bad weather. Tuesday was the last day open for the test under the U.S.-Soviet Intermediate-Range Nuclear Forces treaty.The 56-second test started at 6:35 a.m. at Pueblo Army Depot Activity 15 miles east of here, officials said.

"There was a steady, bright white light from the end of the rocket nozzle extending approximately 75-80 feet," said depot spokeswoman Mary Wilson.

A brownish plume stretched out horizontally before the wind swept it across sagebrush-covered plains and about 50 monitors set out by the Colorado Department of Health, which will analyze the exhaust to see if such firings would pose any threat to the environment.

"The firing was conducted successfully. We expect the test itself will be a success from our initial indications," Wilson said.

The intermediate nuclear weapons treaty was ratified last week by the Senate, and copies are scheduled to be exchanged Wednesday at the summit meeting in Moscow between Soviet leader Mikhail S. Gorbachev and President Reagan.

The treaty requires that the Army's 420 Pershing missiles be destroyed, and the United States plans to destroy the missiles by firing their rocket motors, which cannot be reused.

If the test had not been done Tuesday, it would have had to be delayed by at least 30 days because it would have been governed by the treaty.

"If we were to test fire it, it is then treated as an elimination (of a weapon) under the treaty and subject to inspection by the Soviet inspectors," said Wilson. "They'd have to witness it. . . . We have to give them 30 days' notice for an elimination inspection."

Because the Army stores and maintains Pershings at Pueblo, the installation is the preferred site for demolishing them, but three other installations also are being considered, Wilson said.