Unfortunately, the short answer is no. God of War is a PlayStation exclusive franchise, which means that it has never been released on Xbox consoles, including the Xbox 360.
The direct answer is that there is no legitimate version of God of War available for the Xbox 360 God of War
The God of War franchise is a flagship series owned by Sony Interactive Entertainment. Because Sony and Microsoft are direct competitors, God of War has never been officially released for the Xbox 360.