No. Polar bears live in the Arctic, at the top of the world. Penguins live in the Southern Hemisphere, at the bottom. They have never met in the wild and never will.
Antarctica has no native land mammals at all. No bears, no wolves, no foxes, no reindeer, no musk oxen. The largest visible Antarctic animals are marine: whales and seals.
The reverse question comes up just as often, so: there are no wild penguins in the Arctic either. Puffins, guillemots and little auks look vaguely similar and are often mistaken for them in photographs, but they are flying seabirds and are not related.
If you see an image with polar bears and penguins in the same frame, it is fabricated. It is one of the most common errors in travel imagery, and it tells you something about how carefully the rest of that page was put together.
Someone occasionally raises the Galápagos penguin, whose range creeps up toward the equator. It is a fair piece of trivia and it does not change the answer. The Galápagos are not in the Arctic.