Can marijuana turn your tongue green?

No.

Nevertheless, amaizingly, the California Highway Patrol Driving Under the Influence Enforcement Manual identifies "green tongue" as a sign of cannabis influence. It is also identified as a possible indicator of cannabis use by the National Highway Traffic Safety Administration's Drug Evaluation and Classification Training Program.

The smoke itself does not turn your tongue green, so perhaps the idea is that, for instance, if you are smoking from a joint some amount of unburnt cannabis may find its way into your mouth and the chlorophyll found therein may stain your tongue. Then a green tongue may be a sign of smoking a joint, or drinking green tea or eating celery.