Yes you will, as long as it was a once-off brush with the law. If you had multiple convictions your application for a visa would likely be denied.
You can still travel to the U.S. visa free using the visa waiver program. When completing the Electronic System for Travel Authorization (ESTA) online form that all waiver travelers must complete before coming here, you’ll notice a question in the last section that asks if a traveler has ever been arrested or convicted of an offense or crime involving moral turpitude.
You should respond no to this question, since a single driving while intoxicated conviction does not qualify as a moral turpitude crime. (That’s a whole other area that we’ve examined before in this space; examples of such crimes include murder, drug offenses, rape, assault, etc.)
When you are at the airport and you are completing the I-94W visa waiver form you’ll notice a similar question. Again, the correct response would be no.
Though it should go without saying, drinking and driving can have so many negative consequences, including travel to the U.S. Make sure you don’t do it again, or else your passage here won’t be as easy.