Is there any proof that unicorns exist?

Hunters have searched but no proof, DNA or anything to do with a unicorn has been found so to answer your question no

Answer

Never mind proof, there is no evidence that unicorns exist (or existed) at all. In the philosophy of science there is no such thing as proof, only refutation or the build-up of supportive evidence. Narwhals and oryx are often implicated to explain the inspiration with which humans conjured the unicorn myth. But narwhals and oryx (the silhouette of which looks like a single horned animal) are not unicorns. Evolutionarily, there is presumably nothing to stop a perissodactyl (horses, tapirs and rhinoceroses) evolving a horn. If rhinoceroses have horns, perhaps the horse family can too. The fact is that the horse family just doesn't (and never did as far as we know) have horns.