He is running as the candidate of peace and prosperity, a man dedicated to ending the arms race who argues that not even the U.S. economy can be put right until the threat of nuclear annihilation is eliminated.

He is carrying his gloomy message about the fate of the earth across America--to oilmen in Oklahoma City, to Alabama Gov. George C. Wallace and to small gatherings in Iowa where the first caucuses of the 1984 presidential campaign will be held.

On a brilliant spring morning recently in Cedar Rapids, Iowa, it was clear that Sen. Alan Cranston (D-Calif.) is beginning to be heard.

He had just finished speaking to a breakfast of local citizens, and Jon and Leaetta Wacker had lingered to fill out volunteer cards. The Wackers are not devoted Democrats but are committed to the nuclear freeze movement, and Cranston has attracted their interest.

"I think he's on the right side of the nuclear arms issue, and I would support him on the basis of that issue--no matter what his other positions are," Jon Wacker said.

No one knows how powerful the arms issue will be in the 1984 presidential campaign, but there are indications in Iowa and elsewhere that Cranston's calculated gamble of identifying himself so completely with the issue in his announcement speech may return unexpected dividends.

Through tireless campaigning, a well organized campaign staff and single mindedness on his message, Cranston is working to supplant Sen. Gary Hart (Colo.) as the liberal alternative to former vice president Walter F. Mondale.

Hart is not in the least conceding the peace vote to Cranston, and the two now are dueling in Wisconsin where the Democratic Party will hold a straw poll next month. It was Cranston's surprising second-place finish in the Massachusetts straw poll last month that propelled his campaign, if not into the spotlight, at least out of the shadows.

In Iowa, the freeze movement appears to be growing, with reports that it has taken hold not only in the cities but also in rural areas. Rep. Berkley W. Bedell (D-Iowa) has formed an organization called People Encouraging Arms Control Efforts (PEACE) and has invited all of the Democratic presidential candidates to a forum Aug. 13. He hopes to make arms control a central issue of next February's caucuses.

"A lot of people who show up will be new people, that's what I hope," said Tim Button, Iowa coordinator of the Nuclear Weapons Freeze Campaign. It is an axiom of presidential politics in Iowa that the candidate who attracts new voters to the caucuses springs the biggest surprise.

Cranston has by no means cornered the market on the freeze vote here. But by declaring in his announcement speech last Feb. 2 that ending the arms race "will be the dominating goal of my presidency," he has made freeze advocates pay attention to a candidacy that has been a long shot from the beginning.

"The important thing is that the freeze issue goes beyond what people think of as the peace movement," one Iowa Democratic activist said. "It's middle-aged women and farmers. That's where Cranston's really going to cash in."

On the morning that Cranston's campaign came to Cedar Rapids, county Supervisor Joe Rinas climbed aboard.

Rinas had been in touch with the campaigns of Mondale, Hart and Sen. John Glenn (D-Ohio) but chose Cranston because he admires the senator's "courage to concentrate" on arms control and full employment.

No one talked that way a few months ago. The biggest boost was Massachusetts, where Cranston ran ahead of Glenn, Hart, Sen. Ernest F. Hollings (D-S.C.) and former Florida governor Reubin Askew after spending about $25,000 and campaigning there for seven days.

Cranston has approached each test of 1983 the same way. By concentrating his energies on short-term tests--the California convention in January, the AFL-CIO meeting in February and qualifying for federal matching funds--he has given his campaign credibility.

He is betting that the route to the Democratic nomination is through liberal activists and is blatantly courting all of them--labor, women, minorities, environmentalists, freeze supporters. His strategy risks leaving him stranded out in left field as a political Johnny One-Note, but it may be necessary for a candidate who only registers in single digits in most public opinion polls.

"I will handle it by stressing other issues," Cranston said. "It was a deliberate decision to stress arms control early because I wanted to establish it in my campaign. I will never let it appear diminished because I want it to be out front. It's sound politics as well as sound policy."

Since his announcement speech, which concentrated on the arms control issue, Cranston has elevated the economy and his still undefined call for full employment to equal status. Cranston's economic program still is taking shape. For example, he once considered a 4 percent unemployment rate as full employment but now says 5 percent is his target.

In addition to all of the activists Cranston has never met but is so dependent on, his national staff also is in the hands of people with whom he has had little or no experience.

His campaign manager is Sergio Bendixen, 34, who came to him on the recommendation of the late Rep. Phillip Burton (D-Calif.). A native of Peru, Bendixen first became involved in politics in George McGovern's 1972 presidential campaign. In 1976, Bendixen worked for Jimmy Carter in Florida, then was an organizer for Sen. Edward M. Kennedy's 1980 campaign.

The deputy campaign manager is Tom Pazzi, 35, a former Detroit banker who also is a veteran of the 1980 Kennedy campaign and of Robert M. Kennedy's 1968 presidential campaign.

Cranston's national field director is Paul Ambrosino, 26, who worked for the late Hugh Gallen, former governor of New Hampshire. The campaign's national political director is Mark Cohen, 26, who worked in the Carter White House and later for the Miami Chamber of Commerce, while the press secretary is John Russonello, 28, a veteran of the staff of Rep. Peter W. Rodino Jr. (D-N.J.).

Cranston has hired Mike Rowan of The Rowan Group in New York City as his pollster. Rowan has polled for former Alaska senator Mike Gravel and Sen. Howard M. Metzenbaum (D-Ohio).

John Law, respected former executive director of the Iowa Democratic Party, heads Cranston's organization there.

In New Hampshire, where the first primary will be held in 1984, Cranston's organization is headed by Phil Grandmaison, whose brother, Joseph, is John Glenn's national political director.

Cranston's organization has served him well to date, but it is not fully clear how far his candidacy can be carried on the arms control issue. Nevertheless, he said he will continue to make arms control the centerpiece of his campaign.