There's a tough, chain-smoking liberal running for governor here on a law-and-order platform.

Her name is Roxanne.

Roxanne Conlin actually. But the campaign posters simply say RoXanne. So that's what everyone calls her. And, if the polls are correct, she has a very good chance of becoming the first woman governor of Iowa.

She's a dynamo of a candidate, young, energetic and articulate, the kind who begins the day at a plant gate at 6:30 a.m. and ends it at a union hall at 10 p.m.

Iowa has never seen a candidate quite like her. She's a dedicated feminist, a supporter of the Equal Rights Amendment and legalized abortion, and founder of the Iowa Women's Political Caucus in 1972.

Yet she is best known as a stern U.S. attorney who made her reputation prosecuting bank robbers and crooked politicians. And she still spends much of her time on the stump recalling cases she worked on and reciting her law-and-order platform, which calls for abolishing parole and forcing convicted criminals to repay victims of their crimes.

The Iowa governorship has been the property of Republican Bob Ray for the last 14 years, but he decided not to seek reelection. And this is widely expected to be a year for the Democrats in the recession-pressed Midwest.

Few gave Conlin, 37, much of a chance when she began her lonely campaign for the Democratic nomination 13 months ago. "I told her we'd just had that election a statewide ERA referendum and lost. The liberal-women's agenda had been defeated," state Democratic chairman David Nagel admitted sheepishly. "I thought she should forget about running."

But with only 10 days remaining before the June 8 primary Conlin is the acknowledged front-runner for the Democratic nomination. The latest Iowa poll, published by the Des Moines Register on May 16, found her to be the choice of 44 percent of likely Democrat voters. Former lieutenant governor Jerome Fitzgerald, who lost to Ray in 1978, was favored by 24 percent; former party chairman Edward Campbell by 15 percent.

Conlin also led Lt. Gov. Terry Branstad, who is unopposed in the Republican primary, 45 to 38 percent.

The big danger is that Conlin supporters may become overconfident and she may become overcautious in the final days before the primary. "I'm striving not to shoot myself in the foot," she said last week.

If Conlin were a man there would be nothing particularly remarkable about her campaign. Men have used U.S. attorney's offices as springboards to higher office for generations. Often they've built up networks of statewide contacts through such male organizations as the Jaycees.

But Conlin isn't a man. Her first job in politics was to run a babysitting service for supporters of John F. Kennedy during the 1960 election.

She is among a growing number of women candidates around the country who are products of the feminist movement of the 1970s. Her first statewide network was a feminist one, developed through her work with the women's political caucus and the ERA. Her second was a law enforcement one, made possible by her appointment as U.S. attorney by President Carter. She has also picked up important support from organized labor.

She shares many of the same problems that women candidates have encountered elsewhere. She has had trouble raising money, for example. She began her campaign with a $14,000 loan from her husband, James, a Des Moines realtor, and recently borrowed $50,000 more

When Conlin went to Texas last week to raise money, she visited with other feminists, instead of fatcat oilmen. Frances (Cissy) Farenthold, a one-time gubernatorial candidate, and Houston Mayor Kathryn Whitmire sponsored receptions for her. She collected only $2,000.

Conlin has also been deluged with free advice. Most, she said, "centers on my appearance. People tell me my hair is too long or too short, too curly or too straight, too red or too blonde."

The consensus, however, is that being a female has worked to Conlin's advantage. "People are looking for something different," state party chairman Nagel said. "There's a dissatisfaction with both parties. She's different, first because she is a woman, but she's also a mix of conservative and liberal positions."

Conlin began her campaign earlier than her two primary opponents, and they complain about the favorable media attention she has received. "A lot of people are going to vote for her to prove they aren't biased," said Fitzgerald.

Philosphically there is not a great deal of difference between the three Democrats. All lambast President Reagan's economic programs, and the deep conservatism of Republican Branstad. All promise to create jobs.

The three sounded so much alike during a radio debate last week that the host at one point suggested they considered sharing the governor's job. Campbell has tried to separate himself by proposing an increase in the state sales tax for a year, claiming his opponents have failed to say how they'd pay for the programs they advocate.

Campbell is a respected political operative, who served as an aide to former governor and senator Harold Hughes and former senator John C. Culver before becoming state party chairman. But he has spent his entire career in the shadows of others.

He entered the race only after Hughes, who recently moved back to Iowa, decided not to run himself because of questions about whether he could met state residency requirements. Hughes is now Campbell's most influential backer.

Fitzgerald, a Fort Dodge engineer, started the race late, and has had difficulty raising money. But he is an energetic campaigner, and has made inroads in recent weeks. His big pitch is that he could do more than the other candidates to bring jobs to Iowa.

Without a primary opponent, Branstad might have been expected to sit quietly on the sidelines. But he has begun a major advertising campaign, and begun trying to shed his ultra-conservative image. "I call it my Oklahoma offense," he says. "You start strong and keep building. You keep the ball on the ground, grind out the yards and don't try any go-for-broke passes."

But some Iowa Republicans worry that economic problems in the state could prove disastrous for Branstad and endanger three incumbent GOP congressmen, Reps. Jim Leach, Thomas J. Tauke and Cooper Evans.

"It will be very difficult for Branstad. Iowa has really been hit hard," said former GOP state chairman Steve Roberts. "There is a tendency to blame the party in power. That's a big burden for anyone to carry."