OTOH you can have a conviction for impaired driving and that would have no effect on your admissibility to the United States although anyone seeking to enter Canada would be criminally inadmissible under our immigration law.
However you may be eligible to apply in advance of your travel directly to Customs and Border Protection (CBP) for a temporary waiver of inadmissibility. The waiver application process can be lengthy (up to a year) and there is a cost of US $585.00 per application regardless of the decision on the application. This is discretionary and the US treats all drug possession related cases seriously.
Myles Wilkinson of Victoria learned this lesson the hard way when he was denied entry after winning an all expense paid trip to the Super Bowl in New Orleans.
A Vancouver Island man who won an all-expenses-paid trip to the Super Bowl in New Orleans has been refused entry into the U.S. because of a marijuana possession conviction dating back to 1981.
Victoria resident Myles Wilkinson won the trip in a fantasy football league contest, competing against nearly four million other players for the chance to attend the National Football League championship, featuring the Baltimore Ravens and the San Francisco 49ers.
But when he got to Pearson International Airport in Toronto on Thursday, U.S. customs agents learned of a marijuana possession conviction in Vancouver in 1981 and told him he was not allowed to enter the country.
"I had two grams of cannabis. I paid a $50 fine," Wilkinson told CBC news.
Wilkinson said he was 19 when he was busted.
"I can't believe that this is happening, for something that happened 32 years ago."
Wilkinson's denial of entry into the U.S. is a common story, according to Dana Larsen, director of the Sensible B.C. campaign, a group advocating for the decriminalization of marijuana.
"There's hundreds of thousands of Canadians who have these criminal records for small amounts of cannabis and that results in a lifetime ban for accessing the U.S."
Now that two U.S. states — Washington and Colorado — have legalized the recreational use of marijuana, Larsen is pushing for a similar referendum in B.C.
"Being a cannabis user should not be a criminal offence. It should be regulated and taxed and controlled, but it should not be banned."
Larsen said RCMP have doubled the number of possession charges in B.C., laying about 3,800 charges for possession in 2011.
"That means every day 10 more British Columbians face the lifetime stigma of a possession charge."
Beer-maker Bud Light Canada, which sponsored the fantasy football contest that Wilkinson won, has invited him to attend its Super Bowl party at Vancouver's Commodore Ballroom as their guest Sunday afternoon.http://www.cbc.ca/news/canada/british-columbia/story/2013/02/03/bc-superbowl-fan-denied-us-entry.html
BTW a referendum in BC as being advocated in the story above would have no effect because marijuana is under the federal criminal law power and the Harper government has been clear that it has no intention changing the law.