Republican women are taking the offensive. Stung by the ''gender gap,'' they are beginning to organize nationwide to put across the President's message and turn out the vote for him in November. Their message is a simple one: President Reagan's economic policies have benefited women, and, contrary to critics, this administration has done more for women than previous Democratic ones have.
''There are many perceptions on the part of women that Ronald Reagan is insensitive,'' says Margaret T. Hance, cochairwoman of the Reagan reelection campaign committee. ''It's our fault that such perceptions exist. We haven't taken time to change them and to give our view.''
Now a concerted effort will be made to present that view. ''Women for Reagan-Bush'' committees will be formed in every state in the next few weeks as part of the umbrella reelection committee. Each state committee will have a chairwoman and cochairwoman drawn not only from GOP activists but from professional working women as well. The search is on for teachers, businesswomen , and others to serve on the committees.
Purpose of the new groups will be to rally Reagan female partisans to give speeches - in civic organizations, parent-teacher groups, and other community forums - and line up support for the President.
Mrs. Hance, a former mayor of Phoenix, Ariz., who shares chairmanship of the national Reagan-Bush '84 Campaign Committee with Sen. Paul Laxalt (R) of Nevada, has broad political duties, including working with state and local officials across the country. But she will also try to tap women for the coming drive to woo the female vote. ''We want (women) in the country to know they are welcome in the Republican Party and to share the belief that Reagan's way of improving the status of women is the way to go,'' she says.
A parallel development is the the Republican National Committee's recent formation of the National Women's Coalition, a group of women business executives and other professionals who back Reagan and will speak on his behalf during the campaign. This group has about 40 members and hopes to boost this number by another 40 in the next month.
The gender gap - showing that Reagan has more support among men than women - is misleading, Mrs. Hance says. The latest poll shows a 53 percent approval rating for the President among women. Quips Mrs. Hance: ''As an official who would be happy with getting 50.01 percent - 53 percent is fine.''
''But the perception of a gender gap is important,'' she stresses. ''Women will be voting in record numbers, and where the election is close that could be important.''
Interviewed in her paneled office at the Reagan-Bush '84 headquarters, Mrs. Hance spoke enthusiastically of the gains women have made. Between 1970 and 1980 , she noted, the number of women in managerial and professional occupations grew by more than 80 percent. Ten years ago women accounted for only 43 percent of college enrollments; today they account for 68 percent.
''By 1988 we will probably have a woman nominee for vice-president,'' she says, ''and I hope a strong presidential candidate will be developed for the 1990s.''
Would a federal equal-rights amendment help women advance faster?
Mrs. Hance acknowledges that the feminist movement has given impetus to the drive for equal rights and to ''millions of women who were unsure of their own thoughts.'' But she opposes a national ERA. ''We are already protected by the Constitution,'' she says. ''If we are not going to get an ERA, let's get on with legislative efforts to eliminate discriminatory laws.''
Not all the women in the Reagan reelection campaign are against an ERA. The President's own daughter, Maureen, is a staunch supporter of it. So is Sonia Landau, who is in charge of setting up the Women for Reagan-Bush committees in the 50 states. ''One thing about this administration - we do not all have to be in lockstep,'' Mrs. Hance says.
An issue of growing interest to women is equal pay for comparable work. Many women's groups support the concept, arguing that jobs women traditionally occupy - secretarial positions, for instance - are compensated at lower levels than jobs with comparable responsibility held by men. Recently, a federal judge found that Washington State paid women 20 percent less than men for comparable work and ruled it must grant back pay and raises to women workers in that state.
The Justice Department has considered filing an appeal in the case in an effort to get it reversed. But Reagan political strategists are concerned that such intervention might aggravate the gender gap - though they clearly are unsympathetic to the Washington ruling.
''It's an extremely complicated issue,'' says Mrs. Hance, who as Phoenix mayor supervised some 9,000 employees. ''It could be critical to the whole civil-service system, because supervisors would be making less than those they supervise. So you'd have to upgrade all salaries - or reduce some in pay or have fewer employees.''
''But it does need to be looked at,'' Mrs. Hance adds. ''There ought to be equal pay for equal work. Overall, women are still at 59 percent of the (pay scale for) male workers, and that disparity has to be addressed - whether through comparable worth or constant attention at state and local levels to annual adjustments.''
Mrs. Hance, a mother of three and grandmother of one, says she believes the Reagan record on women is much better than critics allow. She notes that no other president has appointed women to three Cabinet-level positions or to the United States Supreme Court. Also, she lauds Reagan for backing legislation reforms that benefit women.
Mostly, Mrs. Hance stresses the theme that Reagan himself is sounding on the hustings: ''Economic recovery is helping all women and is especially important to the working poor. They will not be helped by a constitutional amendment but by getting into the job market.''