Like two people in this thread have explained, you have two options.
1: Craft/find Arm-splints (leg splints dont count), and keep them on for a few days (depending on your general health, it can take a week or more.) After a while you’ll get a message saying something along the lines of ‘Your left/right arm has begun to heal.’, at that point you can use first aid kits/bandages to increase the limb health back to green.
I’m not 100% sure whether carrying two arm-splints means both arms are healed at the same time, I’m reasonably sure that only one arm/leg heals whilst the other one stays crippled until the other one is un-crippled.
To be able to craft splints you need at least survival level 1 (and First aid?), luckily the resources needed are extremely common.
2: Find a stem-cell treatment console in hospitals. This also fixes all (mutations?) bad traits like Asthmatic and short-sightedness. It does have a small chance of giving a bad result leaving you in bad doo-doo, and well… Hospitals are death traps unless you know what you’re doing.
Best thing to do is find/craft some splints and just hole up in your little outpost until your arms are back to health. Whatever it’s worth, be ‘glad’ it’s your arms and not your legs, because I had two crippled legs (yay, caustics), and they pretty much make you extremely slow and an easy target for anything but crawlers.