A plastic polish/cleaner, like some of the ones already suggested is a start. They are, no doubt, abrasive and will finely polish the plastic until the scratches are less noticeable. If you're unable to find a cycle shop with the product suggested, try going to an airport FBO or pilot-shop and find some airplane windscreen polish or the Meguires "Mirror Glaze" as was also previously suggested.
Finally, if the scratches are getting deep and you're noticing a significant hazing because of their number you might consider getting a plastic restoration kit. These kits aren't based on liquid abrasives like the polishes, but rather are a set of very fine sandpapers that start with a fairly heavy grit and end up with a grit similar to heavy paper - finishing off with a liquid polish. I've seen plastic windows restored from nearly opaque to perfectly new-looking using these systems (the Smithsonian uses them, as do airlines and airplane restorers, among others).
My experience is with "MicroMesh" but I think there is at least one other brand out there.
Sorry, I couldn't find a company web site - but this one has some brief info:
https://www.aircraftspruce.com/catalog/cspages/micromeshscratch.php
Incidentally, if you're curious at all about this process and don't want to buy it just head over to your local drugstore and look through the cosmetics section. If you look around you'll find a finger nail polishing stick made by Revlon (looks similar to an Emery board only thicker and soft). Buy it and follow the instructions. The different abrasives used by Revlon are virtually identical to the window restoration kit, and the results are just as amazing.