Is there any evidence for a war on Mars involving the Anunnaki?

There’s no reliable evidence identifying a war, a side that started it, or survivors who came to Earth. Mars has been studied extensively, but no confirmed cities or signs of an ancient civilization have been found.

The Anunnaki appear in ancient Mesopotamian religious traditions as deities. Those sources don’t establish them as an extraterrestrial people who lived on Mars, enslaved humans, or fled a planetary war. Connecting those ideas is a modern speculative interpretation, not something the ancient texts confirm.

The idea that human beings became cave dwellers after such a war also doesn’t match the evidence for human origins and development.

If you mean it as a story premise, you could choose an internal conflict, an outside attack, or a disaster that later got remembered as a war. But those are creative possibilities, not answers supported by evidence. For a factual account, the honest answer is that the war and the Anunnaki’s fate aren’t established.