In practice, no. Just pretend it never happened.
If you stick rigidly to the rules it depends what that 'minor ' offence was. Moral turpitude is their criterion, which means (very much oversimplified) that you did something with evil intent. Nothing to do with 'minor' or 'major' Stealing a mars bar is moral turpitude just as much as robbing a bank.
The US London Embassy website is not very helpful on this - they err very much on the side of encouraging you to apply for a visa whether you need one or not.