Can you make nail polish out of acrylic paint?

Yes, just fine. Just be sure to use student grade (low quality) paints instead of artist quality. The artist quality ones have a more rubbery texture when dry and tend to peel off. Mix any color and use a clear topcoat to seal it (necessary). Be careful with yellows and Oranges, they're more likely to stain your nails if you have them on for long periods of time. To prevent any staining, use a base coat to protect your nail.