Mrs May said she planned to allow victims to choose the penalty imposed on criminals, including replacing damaged property, paying compensation or simply saying sorry.
She pledged home owners should no longer feel "powerless" against offenders, and promised to "put the victim first".
In an interview with the Daily Mail, she said the new powers, which will be outlined at the Conservative Party Conference today, would be used for low-level crimes to give victims a "say".
"One of the big problems for the victims of anti-social behaviour is that they feel powerless,' Mrs May told the newspaper.
"Somebody does something to them or their property and they feel they don't get reparation, or feel they are not part of the process.
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"We want to ensure that they have a choice.
"It will mean saying to the victim: here's a list of options, what do you want to do?
"They may choose to go down the restorative route, and that they want someone to say sorry."
She added they could also stipulate the perpetrator repaired property they had broken, or carried out work in the community.
If criminals refuse to accept the conditions, they will be subject to normal court proceedings.
It is understood the options for punishments, called the "community remedy" will be laid out in a menu-style list for police commissioners to work from.
Mrs May added: 'It's also about giving victims transparency.
"One of the complaints I hear very regularly from victims is that they have reported an incident to the police but they don't know what happens after that.
"It's about putting the victim first. They've suffered and they should have a say in what happens."