How do I enable the option in League of Legends, which enables a large arrow upon my character when pressing space to center the camera? Is it even in the game?
Open the options menu with esc and go to the Interface tab. In the Notifications section, there will be a checkbox labelled Champion Highlight on Camera Center. Just check it and every time you center your camera, there will be an arrow indicator on top of your character.
There is no official announcement of this feature, but it appears that it was released on patch 6.24.
As far as I know, there is not arrow that will be over a character's head. If you want to lock the camera on your character, you will have to enable the camera lock in settings or toggle it with Y (the default key to toggle camera locking). If you have a image you could provide, it would help.
Edit: The latest patch (7.1) and above should let you center your camera and have an arrow above the character's head.
There is no such Feature in the game but I could think of two things that you describe.
A visual indicator to a debuff (Nautilus R, Vi R, etc.) that got changed to an arrow by a (custom) skin.
A 3rd party program that highlights your character if you center your camera.
Now while the first one is in a greyzone the second one is definitely forbidden to use, since Riot doesn't allow software that meddles with the game itself.
The only indicator that is in the game by default is a small circle around your character in some custom game modes like Hexakill or One for all.