We all know that Constantine is being dusted off in Arrow, after some IMDB search we know that Constantine will be coming to only 1 episode and that is Episode 5 of Season 4 called "Haunted".
There are many theories out there, what could Constantine do in Arrow.
The Lazarus Pit
When we first found out that Constantine was coming to Arrow, we all thought Lazarus Pit because it's the main "magic" source in Arrow. Maybe Constantine is there to destroy it, maybe to help Arrow use or understand it? Arrow since he found the Lazarus Pit has not yet understood how it works or what it really does to people who have used it. It has been stated that Lazarus changes a human after he has used it, but to what degree? Maybe Constantine can shine some light on that mystery for us and Arrow.
I almost wrote Damian Wayne there. So as of Season 4 we have a new main Villain, a magic user called Damien Darkh who seems to be on a very high League stopping arrows in mid air. Not only do we know that he possess the Jedi power, fast enough to stop arrows mid air, he can also kill people by just touching them. Since Damien Darhk is credited in the last episode of Season 4 we know that Constantine isn't coming to help Arrow defeat him, so maybe just teach about magic? Who could be better person to teach about magic than Occult Magician Constantine himself.
There are more fan theories out there, but they were made before his episode count was public and none of the others wouldn't really make sense for him to only appear in 1 episode.