Can't reinstall the Camera icon on my iPhone
You actually can't remove the Camera app, but you can move it. Perhaps it is hidden in a group.


Go to Settings -> General -> Reset and tap "Reset Home Screen Layout".


"Camera" should reappear in the first page, but if it doesn't its likely a parental control or a profile restricting camera use. 


Go to Settings -> General -> profiles and delete all of the ones you don't need. Inspect the ones you wish to keep to see if one restricts the camera. 


If that still doesn't work, you'll want to back the device up and restore it to get if a hardware or software problem is causing the problem.