No. It is hydrogen fusing to helium. It should have a small amount, just as there is on Earth, of the more stable isotope Plutonium-244  with a half life of 80 million years, which must have been created in supernovae, and was present in the nebula that condensed to form our solar system. The sun has all the naturally occuring elements we have on Earth.  See also: Do transuranic elements such as plutonium ever occur naturally?

Though, see Mehran Moalem's answer to Is it true that the core of the Sun is Plutonium? - perhaps even the minute traces of Plutonium 244 would burn up also. It would have really tiny amounts surely from materials that hit the sun, must have minute traces of everything you find in the rest of the solar system but seems it would be depleted in Plutonium 244 even relative to the minute amounts we have elsewhere.

Our sun won't go supernova so it will never make plutonium 244 for itself. You also get  plutonium 239 in a naturally occuring nuclear reactor on Earth. But it rapidly decays so that after two billion years, there is almost none left, though they can tell it was there by its decay products. The Workings of an Ancient Nuclear Reactor.

But the sun's core is seven times denser than plutonium, perhaps that's what you are thinking about? It's got a density of 150kg/liter or about seven times denser than platinum.

But the outer envelope - what we see, is much less dense. Even 2,000 kms below the apparent surface of the sun, the sun has about a thousandth of the density of the Earth's atmosphere at sea level. Though the gravity is huge, so also is its temperature and the hot gas expands and it's average density is much less than the Moon.

When the sun runs out of fuel it will become a white dwarf, with a density of a million tons per cubic meter. So that's the density it would have it wasn't so hot, temperature currently 27 millions of degrees - in white dwarf stage will be "only" a hundred thousand degrees or so.

You might like my Is it possible to build a human suit or spacecraft that can travel through the sun without being affected? If so, what would one be made of and how would it work?  just for fun :).