Yes, but most people would think that you study it as a subject at uni. That’s the most common meaning of it when you use it in the ”study” sense. :) But you could specify with something like ”Jag läser svenska på egen hand” (on my own).
Couldn't study be Studera? I only ask b/c of the song lyric from "De Mördades Fria Republik": Studera Marx och Lenin och Förena er!