What iOS Twitter apps support custom API URLs?
Tweetbot for iOS does. It relies on the "tweetbot://" prefix. Using it without a suffix launches the app. But you can also tack on things like "timeline" to load up a users own timeline (the full command would be as follows tweetbot:///timeline). Other commands are tweetbot:///post?text=hello which will tweet "hello" or tweetbot://cksum/post which will tweet with a username (in this case "cksum"). Others include things like search or pull up a user's profile.