Hmm I'm not exactly familiar with it myself, but you should be able to.
You can take the screen snapshot and pass it to the system share function for mobile, and they would select Twitter manually if they have it installed. The example editor.construct.net should get you most of the way there.
If you want to use Twitter directly I imagine Twitter has a JavaScript API that you can access directly via scripting actions in c3 to authenticate and upload to Twitter, but I'm even less familiar with about how to go about that.