Just ask her, which scenario would be preferred? You unknowingly are in the wrong place at the wrong time one day (which can happen to anyone) and become a victim and are killed or seriously injured because you had no way to defend yourself, or you were (unknowingly) in the wrong place at the wrong time, but had a means of self defense and were able to utilize it and live to tell her about it? Which phone call would be worse?
Of course you have to back this up by showing how you always carry responsibly and explain what carrying responsibly means to you (i.e. things like going out of your way to de-escalate or things of that nature).
If this doesn't work, then it's possible nothing will. I know the feeling of disappointment or misunderstanding by parents can make you feel bad even as an adult yourself, but hey you are an adult, and your moms gonna love you whether you carry or not. Time may be a factor here to, if over time you show your not gonna mess up or go looking for trouble or things of that sort, quiet possibly she may warm up to the idea. I have gone through this same thing with my mom in the past, and she says of course I would rather you have a means to protect yourself if that time ever came, but I just worry. She's a mom it's what moms do.