Actually, I haven't had any trouble at all putting style sheets into a Raw HTML component in Studio. I just tell it
<link rel="stylesheet" type="text/css" href="/static/predictionx.css" />
and it works, despite not being in the "head" for the page.
Alternative method: use javascript or JQuery (since it's in edX already) to to inject a style sheet into the "head". Maybe not the best idea, but I'll let you decide that.
https://stackoverflow.com/questions/5680657/adding-css-file-with-jquery