Tens of thousands of West German demonstrators joined in nationwide protests against the nuclear arms race today in a bid to revive the country's dispirited peace movement.

Organizers claimed that more than 300,000 people, including former chancellor Willy Brandt, turned out at various rallies to show their opposition to high defense spending and the continuing deployment of U.S. Pershing II missiles. Police put the number of demonstrators below 150,000, news agencies reported.

The focal point of the day's activities was an attempt to form a human chain 130 miles long, stretching from a planned cruise missile base in Hasselbach through the capital to Duisburg, a depressed industrial town in the Ruhr district with the country's highest unemployment rate.

Several huge gaps appeared north of Bonn, severing what peace groups had promised would be "the longest human chain in history." In other places, people unfurled long antiwar banners to extend the links between hand-holding demonstrators.

Today's demonstrations occurred one year after a climactic week of peaceful rallies that brought hundreds of thousands of West Germans -- some reports said more than a million -- into the streets in an unsuccessful campaign to thwart the stationing of new nuclear missiles here. Rallies in 1982 also drew considerably larger crowds than those taking part in today's scattered protests.

Despite the demonstrations, the West German parliament last November approved the decision to start deployment of the missiles, designed to counter the Soviet buildup of SS20 rockets in the absence of an arms control agreement limiting medium-range nuclear weapons in Europe.

Since December, the U.S. Army has installed about one-half of the 108 Pershing II missiles scheduled to be deployed in West Germany by the end of 1986, defense sources said.

In the meantime, the unhindered basing of the Pershing II missiles in West Germany has instilled a pervasive sense of apathy and hopelessness within the movement.

Attendance at rallies and demonstrations this year has consistently fallen below the expectations of organizers. And to the relief of Chancellor Helmut Kohl's government, radical opponents of the missiles have not undertaken a sustained campaign of violent sabotage, something that initially was feared by the authorities.

Several leaders of the crusade against nuclear weapons, such as American-educated Petra Kelly, have complained about feelings of "exhaustion" afflicting people after the long, disheartening struggle to keep the new missiles out of West Germany. Many activists have directed their time and energy now to more personal pursuits or local interests, such as measures to protect the environment, Kelly said in a recent interview.

In Hamburg, a police spokesman said about 15,000 people attended a downtown rally, although organizers had forecast a turnout of 160,000. Another human chain, in West Berlin, drew only 4,000 people, according to police.

In Stuttgart, an attempt to line up people in the form of a massive peace symbol failed to attain planned proportions when only 20,000 out of a predicted 70,000 participants showed up.