You mean DWI as Driving While Intoxicated?
DWI is not consider a crime but it is against the law. As far as I know, it doesn't make you a criminal unless you killed someone while driving. Mostly it showed how bad and irresponsible driver you are.
Will it become a problem? It will depends how serious your offence is. Did the police just caught you in the street and gave you a citation, or did the police suspend your liscence, or did the police arrested you and put you in jail?
DWI or DUI is quite common in the U.S. It mostly will affect your driving record and your driving privileges. If you have been arrested, you need to show to the immigration officers the police record when you're arrested and also the court order . Show these documents when they ask you if you have been arrested and try to explain to them.
I can't tell you if it cause any problem for the process. It is for the immigration officers to decide. All you can do is prepare all the paperwork from that case.