There are a couple of different ways to do this, and hopefully other community members will chime in.
One of the simplest ways would be to create a virtual switch which represents the Arduino. Then its status would show up in the SmartThings app.
So now you’ve got a virtual switch and you want to create bidirectional communication.
For anything complicated, see the developer docs at the link at the top right of this page.
For just a simple on/off, you can use the free IFTTT maker channel as a “man in the middle.”
You have your device send to the IFTTT maker channel as the “if” in an IFTTT recipe and use turning on the virtual switch in the smartthings channel as the “that.” Set up a separate recipe for the off.
You can then do exactly the same thing in the opposite direction: have turning on the virtual switch in the smartthings channel then send something via the maker channel as the that. And again you would need two recipes, one for on and one for off.
The big question with IFTTT is always how much lag Will there be? At my house it’s a pretty consistent eight seconds, which works for most of my use cases, but it varies from person to person and some people have a lot more lag.
The IFTTT maker channel method probably isn’t what you want to do in the long term, as there are more direct methods, but at least it would give you a proof of concept and some initial functionality while you’re looking into the other methods. 
And eventually you would want to write your own custom device type handler for the virtual switch so that you could have the appropriate labels (open/close instead of on/off), add some capabilities, etc.