Speaking during a tour of the Leeds factory, the Prime Minister said she was in favour of the outlawed activity but MPs would be given the final say.
David Cameron had promised to put the divisive issue to Parliament but did not go ahead with the plan due to a lack of support.
Mrs May said: “This is a situation on which individuals will have one view or the other, either pro or against.
“As it happens, personally I have always been in favour of fox hunting, and we maintain our commitment, we have had a commitment previously as a Conservative Party, to allow a free vote.
“It would allow Parliament the opportunity to take the decision on this.”
The Prime Minister was speaking during a visit to Morley, a marginal constituency where Conservative Andrea Jenkyns snatched the seat from Labour’s Ed Balls just two years ago by just 422 votes.
Mrs May took questions from workers on everything from NHS funding to the impact of Brexit, and helping young people get on the housing ladder to high childcare costs.
The Q&A was in stark contrast to Mrs May’s last trip to Leeds less than two weeks ago, after which she faced criticism for not engaging directly with ordinary voters.
Asked why she had chosen to visit Leeds again so soon, she said: “I’ve got a very simple message. Every single vote in this election counts. Every vote for me and my team will strengthen my hand in the Brexit negotiations to get the right deal for Britain from Europe.
“Every vote counts, every person counts and every community counts. So I’m very pleased to be back in Yorkshire, and you never know, you might see me back again before June 8.”
Among the questions put to Mrs May by factory staff was concern about high childcare costs affecting working families.
“Jeremy Corbyn says he will put (minimum) wages up to £10. That’s the only thing that’s going to help us out,” one worker told Mrs May.
The PM responded that “extra support” was now available for families, but acknowledged that “we have to ask ourselves whether it is having the impact we want it to have”.
She added: “This is why it’s so important to have a Government that ensures you have a good economy.
“Whatever Jeremy Corbyn says about the levels he would like to see pay being at, the plans he has got would wreck the economy. Absolutely fundamental to everything is making sure we get the health of the economy right.”
Speaking earlier in the day, Mrs May also put her renewed backing behind a drive to tackle ‘fake news’. She stressed the importance of real journalism and said a free press was one of the “important pillars of our democracy”.