Twitter Image sharing for web applications (API?)

Hello I am making a web application in which users will have to upload images they take to twitter using an integrated twitter image sharing button or function. I have looked at the TwitPic API, which does namely that, but according to their website (http://ift.tt/1eijURJ) they are basically discontinuing the it.

My Question is if there is an API or way in which I can have users share their image to twitter from within a browser window (so that i can be done via mobile devices as well)?

So far I have just used the twitter button creator and created a normal tweet share, but it does not support image sharing or I cannot seem to figure out how to make it support image sharing.