You can be refused US entry due to a past drug conviction or simply for admitting to have done drugs in your past. The current US border policies are long overdue for an update. As this article points out: "There's no reason to believe America is safer when we exclude or harass foreigners who are honest about drug use—and that's the only thing this policy achieves." Read the complete story: Why is it Still Illegal to Visit the US if You Admit to Using Drugs?