Hi, Dusti, and welcome to Pet Talk!
That's normal behavior for any kitten, not just Angoras. She needs to learn to play NICELY with humans. Give her toys she can use her claws on, but any time you feel claws or teeth on YOU, step away, pick your arms up, and stop play. Never, ever do like some people do and play attack games with your hand. She can control whether her claws are in or out. Play with her a lot, "fishing pole" type toys, little cloth mice you can throw for her, and motion-type toys are great. A tired kitten is a happy kitten, and cloth mice, unlike you - do not bleed!
Kittens are fur-covered, so when they play with littermates, claws are okay. She needs to adjust to you, a fur-less human!
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