If you are a Mac user, you can run Splitweet as an application using Fluid.app. It won't take you more than 2 minutes to configure it, and you'll always have your tweets at hand. With Fluid you can have any website configured as an independent application.
To make it work you only need to download Fluid.app, run it and fill the form as shown in the picture:
If you use a different language other than english, put the subdomain in the address for a quicker access. For instance, http://es.splitweet.com if you want Splitweet in Spanish. You can use our ninja as the icon to make it look better (Save this image in your desktop):
And that's all!
If you are a Windows user or Linux user:
There are 2 options: You can do the same using Chrome (win only), but I haven't tested it yet. As a second option, a Splitweet user, Soroush, has reported that Mozilla Prism is doing the same, you can read that in his blog. Download and share your experience to others!