The camera app isn't something you can delete. Try restarting the phone (turn it off and back on) then tap and hold anywhere on the background of the home screen. You should be able to find the camera icon. There should also be a button on the phone that will access the camera as well.
Should restarting not be enough, then try going into "Settings"... "Apps"... "All" and locate the camera app. Tap it and then tap clear data. Warning this can remove photos. It 'shouldn't' but I have seen it happen before. So you may want to back them up first. Once this is done, again restart the phone.
Should none of this work, then I would start to wonder if there is a bad app, virus or malware on the phone that is causing the problem. Either that or...