Impossible on Xbox 360. No built-in option, console command, or mod allows race changes mid-game. Only possible on PC via console commands (showracemenu) or mods (RaceMenu).
Why?
Console modding is extremely limited (no external asset loading).
Race affects starting stats, skill bonuses, racial powers, and NPC reactions—core to character identity.
Alternatives
Start a new game with desired race (fastest with alternate start mods on PC).
Role-play your current race differently (new motivations, backstory, playstyle).