Buff out scratches?

Can I get rid of scratches on a face shield? 

Yeah you can try to buff it out - if you're good maybe not too bad but depends on the depth of scratches.  I got a buddy who can take scratches out of anything.  ANYTHING.

Any recomendations for what I could use?

I think he just uses a buffing wheel and some compound - don't hold me to it... I'll hit him up tomorrow and see what he uses.

There are lots of things from auto stores that will do a decent job, but the things to go for are made specifically for perspex. I use a product called Meguiar's Mirror Glaze, followed with a good quality liquid car polish. I apply both of these using a sponge. Which have to apply it evenly of course, and use a very soft cloth to buff it or you will end up with a swirl of very scratches. A lot of boat places & aircraft hangers have good products to, for the same reason, they use a lot of perspex on their machinery.