Depends on how deep they are. Look for Meguiars clear plastic cleaner and polish. There's also Plast-X that does an OK job. But if they're too deep, nothing is going to fix it.
you can try what Bassquatch says first. If that don't work you can sand with 220 grit all the way up to 1000 grit then flame polish with a propane torch. Make sure that it is Pleiglass (acrylic). If it is Polycarbonate (Lexan) it will not flame polish out. Good luck.
Found out today that it is Lexan, wondering if that would be harder or easier than plexiglass? I grind stumps and it's on my stumpgrinder and what I look through when grinding. All the time getting hit with debris. I replaced it several yrs. ago with a new piece but it was expensive. Just trying to save a little money if I can.
Harley this Novus plastic polish and compound works well. I use it weekly to buff scratches out of lexan. Sometimes I'll chuck a buffing pad in a drill to speed it up. Also works on Jeep soft top windows.
You could try toothpaste. I polished a scratch out of my plastic watch crystal with it. It aint perfect, but, you'd have to really look to see what was a deep scratch.