(assuming pot originated in the New World).
I thought that the ganja was from India. (I see that Ernest beat me to it.)
Anyway, Shakespeare died in 1616, and at that time the English weren't yet sending soldiers and thieves to the East. When they finally got around to it, it wasn't ganja, but poppies that they really liked. Well, that and tea.
Then again, very few compounds have the same retention times and ion products as THC in a GC/MS experiment. The only one that I can think of off the top of my head is a canabinoid called dronabinol, and it also comes from the herb, so who knows? Maybe the bard was toking it up in his dugout.