There's an IFTTT and a Chrome extension that do just that
While Twitter and Instagram are battling out over who gets to control more of what you do online, some users have resigned themselves to not being able to share photos on Twitter, not as easily anyway.But some are looking for solutions and luckily for them, there are options, several of them in fact.
The reason is that, for the time being, Twitter and Instagram both provide rather comprehensive APIs.
Even without APIs, as long as both photos and tweets are public, there's not much Instagram or Twitter can do to prevent people from putting them together.
IFTTT recipeThe first example is an IFTTT recipe which tweets out Instagram photos if you choose to. IFTTT is a very interesting service that glues together the APIs of several big websites and makes it possible to create cross-service automated tasks.
For example, you can set it up to save a photo you tweet to Dropbox, or text you when it's going to rain. It can also tweet an Instagram photo, complete with the actual image.
There's now a recipe for that, enabling users to share their photos on Twitter as long as they include the #twitter hashtag with their Instagram posts. You have to sign up for IFTTT for this to work.
The InstaTwit Chrome extensionBut there's another solution, an even simpler one, as long as you're using Chrome. InstaTwit is a Chrome extension that does one thing, it adds Instagram photos to any tweet with a link to one.
The photos will look and work just like they did before. The extension also works for any photo on Twitter and once you've installed it, there's nothing else you have to do.
The downside, compared to the IFTTT recipe, is that this only works for you, others will still only see a link in your tweets. On the upside, it works for any photo, not just your own.