On what grounds are you trying to relocate to the USA? In general, UK citizens can't emigrate there. Unless you've got exceptional talents which can't be replicated by a US citizen (such as being an international sportsman, a leading actor or a professor of medicine) or immediate family in the USA, you might as well not waste your time.
If you do qualify for (possible) entry to live in the USA, a drink-driving conviction doe not count as 'moral turpitude' (which under the terms of the US Immigration and Nationality Act, automatically prohibits anyone from entering the USA). The USA doesn't recognise the UK's Rehabilitation of Offenders Act, so your conviction will never be 'spent' in the eyes of the US authorities, but it's unlikely to be a bar to you obtaining a residence visa if you're otherwise qualified to receive one.
Chris