I don’t know, but she’s probably way older than you.
She may be in her 60s or 70s, which means that if League of Legends was released in 2005 (when it is assumed Annie was created), then she would have been born around 1963. It’s also possible that Annie has no age whatsoever and exists outside of linear time as a force for good like the Force or light saber badasses who fight for justice against evil empires with laser beams instead of guns or bombs because they’re too classy for that kind of violence. Who knows? Maybe she even flies into my bedroom at night and rapes me with her mind powers before flying off to save some more universes from themselves when I’m asleep