It depends. In the US, there are legal protections against discrimination on the basis of disability, and since self-harm is a symptom of mental illness, that falls under the ADA guidelines. However, if a dress code requires long sleeves for everyone or something similar (basically, the rule somehow applies to everyone, regardless of dis/ability), then I believe it's legal.

What you're more likely to come up against, though, is whether it's really worth a fight. Law or no, some people are likely to be jerks if they see scars, and a lot of the time it's just easier to keep them covered than to get into it with those people. But that's a judgment you can make yourself.