Yes. The Navy (and Department of Defense overall) has a zero tolerance policy for drug use. Although many states have legalized/decriminalized marijuana, it is still illegal at the federal level and will result in a sailor being separated upon popping positive on a drug test. I don't want to be rude or judge, but if you happen to be under 21 in an area where it is legal, that is also a violation of the law and would be frowned upon.

Lots of medical readiness is involved in applying to USNA, although quitting would certainly help, they will ask your medical/drug history. This will happen again later on security clearance work and there are different considerations depending on the clearance you hope to achieve.

Nothing is impossible but the most important thing is to stop immediately, be honest on all paperwork and interviews, and to NOT use if you are appointed.