"Drug charge" can mean anything from simple possession to trafficking of kilos. It matters.
You may want to add that information in the "additional information" section.
I've also reclassified this as an immigration question.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
You need to consult with an immigration lawyer in your area ASAP for advice and direction. We have several avvo lawyers here who practice immigration law that may respond, I'll defer to them.
I am trying to give you a general answer to your question. We do not have an attorney-client relationship by this response on the avvo website. I have not been retained to represent you. I am licensed to practice law in Kentucky and in federal court in this state and the Southern District of Indiana. You need to seek legal advice from an attorney licensed to practice in your area..
I'm really sorry to hear what your cousin has been through. I hope he's doing well. Unfortunately, I think more information is needed to evaluate your cousin's prospective case. He should get a free consultation from an attorney with a good amount of U visa experience. Many attorneys, myself included, can do the consultation over the phone. All it'll cost is time.