Not without some trouble. In Canada a DUI is a felony so they consider it as a serious crime and don't want our drunk driver's there. If it's very old, say 25 years or so, the border agent may let you in anyway. If it's within the last ten years or so there are several different ways you can still get into Canada but you'd best get an immigration attorney's help with that. I'd recommend trying Seattle or Vancouver or go to your nearest Canadian consulate and ask them what to do.
I agree with Mr. Kaman. Although a DUI conviction is relatively common here, it is a bar to entry into Canada. There is a process by which you can petition to have this condition removed, and an immigration attorney can advise you regarding it. Please note that process may take some time. I suggest searching on AVVO for an immigration attorney near Long Beach. Good Luck.
Technically the answer is definitively NO. Canada considers DUI a felony and if and when they catch it at immigration they could very well put you back on a plane and/or turn you around and send you right back to the States. To be safe, you should contact your local Canadian consulate. There are ways to get past it.
The other lawyers here provided you with great answers. If the DUI conviction is old, the person should consider having the conviction expunged by the court. I would also highly recommend that the person hire an immigration attorney.