How old is she? If she's still a kitten it's only natural for her to use her claws when playing. She's not yet learnt that people don't have a layer of fur to protect their skin! Have you tried trimming her claws so that they aren't sharp?
First of all, learn how to trim nails and keep them trimmed short!
Most people make the mistake of pulling away when a cat scratches - that just kicks in the instinct to grab with claws so the "prey doesn't get away". Instead learn to just STOP moving your hand/arm and let others know.
Also, try hissing at the cat (use their language) and walk away. Some cats are super sensitive with touch and can't take a lot of petting at one time.
Well you shouldn't be playing with the cat with your bare hands if you haven't figured that out already since she is a scratcher. You have to use toys not your hands. Especially when they are young and you need to still train them.