Mashable has a post about 5 Ways to Share Images on Twitter. Under some of those ways there are several services listed, in all there are about a dozen.
In the comments someone mentions SnapTweet that works in combination with Flickr.
Personally I am not keen on giving my Twitter password to other services. That means I will most likely provide a link to a Flickr photo instead of using any of the services listed at Mashable.