No joke of the day applications exist for political humour. There are applications that contain political jokes, but these applications do not have a daily joke. Traditional jokes as well as memes are available for download depending on personal preferences.
There are a few good applications on various system markets. "Political Jokes" created by NCPL Inc is one of the top rated. The contents are mainly in the style of memes. They are categorized in the app store as comics. Another high rated app also called "Political Jokes" created by BejuApps contains jokes in the traditional style. This app has no photos, rather a straight forward approach using text only.