No, no one has claimed Antarctica yet.
Many countries have claimed 'slices' of Antarctica, but The Antarctic Treaty defines the area south of 60 degrees south latitude as dedicated to science. The Antarctic Treaty is the only form of governance in this area of the world.
The countries that have exuded claims over parts of the continent have issued postage stamps to support their claims. Some hobbyists have developed 'Antarctic money' as a way to sell Antarctic artifacts. Many scientific stations on the continent fly flags of their sponsoring countries, so you will see flags in Antarctica, but none for the continent itself.
You can read more about The Antarctic Treaty using the link, below.