Thread.sleep in a separate thread would do that.
If you're not making use of AsyncTask for other things use that instead. It will simplify things for you. AsyncTask will make use of a a threadpool, so you needn't worry about creating a thread yourself.
Be sure not to sleep in an event callback for a button or equivalent as you'll be sleeping on the UI thread. That will make your app appear unresponsive and sluggish. Only sleep in some other thread, and invoke back to UI to update.
Edit based on updated Question:
Looks like you're performing some animation on the UI. A separate thread would be best for this as it looks to be a long running process.