Can magic mushrooms be prescribed to you?

No.
You could simmer a large amount of magic mushrooms in water, fresh or dry, and extract the active ingredient, and inject that into your arm, but I'm not totally sure what would happen.

So the question you really want to know is, can you administer psilocybin intravenously.
Yea, you can but the effects would probably be different, i.e. different on-set, peak, come down, but eating them is a much safer, healthier way to take magic mushrooms so I say stick to that if you want to partake.