The US embassy website states that anyone who has ever been convicted of any offence (except minor motoring offences, such as speeding) or even simply arrested (even if totally innocent) is ineligible to travel under the Visa Waiver Program. So, 'officially', you need to apply for a visa.
The visa application process is extremely long-winded. It typically takes around 5 to 6 months. Details of the procedure are in my posts, here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
(To get the links to work, please read the last post first).
However, the actual Visa Waiver form (which travellers complete on the plane), doesn't ask about arrests. It only asks whether you've ever been convicted of a crime 'of moral turpitude'. (The definition of crimes of moral turpitude excludes drink-driving). So you could honestly answer 'No' to the question on the form.
The US immigration authorities have no direct access to UK criminal records. The UK authorities do pass selected information on to them but a conviction for drink-driving would not normally be show up on US records. So it seems likely that you could enter the USA under the Visa Waiver Program, without lying, even though to do so would be in contravention of the rules specified by the US embassy.
Chris