It's not in the app store (yet!), but you can add it to your home screen next to your Clock/Alarm, just like an App Store app.

Open the site in Safari on your iPhone (sleepy.im), then hit your share button on Safari's menu (aka the square with an upwards arrow). You should then have an option to "Add to Home Screen". You can make the name shorter if you like, then tap to Add the icon to your home screen and move it around like any other app.

Hope that helps!