I have never done it myself, but there appears to be an API (or something at least) for handling files being dragged and dropped into a Godot game. This issue has a example project for Godot 2.1. If you are using Godot 3.0 you may need to make some changes.
Here is a Reddit page where someone posted a minimal example, though I think it is using Godot 2.1 as well.
Unfortunately that is all I could find. Hopefully it helps :smile: