To get scratches out of acrylic, I recommend starting with a clean surface and using progressively finer sandpaper — for example, 800 → 1200 2000 grit and then buffing with a dedicated plastic polish.
If the scratches are minor, you can skip sanding and just use a polishing compound like Novus 2. For deep marks, wet sanding is essential before polishing.
Avoid flame polishing unless you have experience, as overheating can cause cloudiness. Always finish with a microfiber cloth to achieve a smooth, clear finish and prevent re-scratching.