The App Store app cannot be deleted. Most likely you either moved it to another Home screen or dropped it into a folder. You can do a search for it, or you can reset the Home screen layout in Settings -> General -> Reset and that should get it back. You may have also inadvertently disabled installing app in the General -> Restrictions settings; check there as well.
Thought my App Store icon was also missing. Found it in the Utilities folder. 1st page only holds 9 icons and didn't know there was a second page. Just swipe the first page of the utilities folder to get to the next page just like you do to get to any additional page. I found the location of my App Store icon by going to Search iPhone. You can find Search iPhone by pulling the icons down on the main screen. But not from the top. That will bring up your calendar, alerts, etc. Your Icon may be hiding somewhere other than in the Utilities Folder. The Search will show you where. This explanation may be more basic than you need but hope it helps!