What iOS Twitter apps support custom API URLs? I recently read about the WordPress.com Twitter API released in 2009, and I want to test it out. 

The API requires you to use a Twitter client that supports custom API URLs.  The example iOS application that they listed was Tweetie2, but it's dead now. 

Are there any other iOS app that allow custom API URLs to that I can test this out?
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.