No. Marijuana is still illegal under Federal Law. This means that even if you have a prescription card in your name, you are not allowed to ship it. Perhaps that will change in the future but for right now, that’s how things stand.
It doesn’t mean that it doesn’t happen all the time though. When I was a postal employee I came across the stinkiest box ever. Whoever tried their best at sealing it must’ve forgotten a section because that thing reeked. In cases like those, the Postal Inspectors are called. They retrieve the package, do some homework, and will eventually pay the shipper a visit.