Can You Play Zelda on Xbox 360? No — Nintendo Exclusive

No. The Legend of Zelda series is a Nintendo first-party franchise exclusive to Nintendo hardware (Switch, Wii U, 3DS, Wii, GameCube, N64, etc.). It has never been officially released on any Xbox, PlayStation, or PC platform.

Similar Games on Xbox 360

• Action-Adventure / Exploration: Fable II / III, The Elder Scrolls IV: Oblivion / V: Skyrim, Dark Souls, Kingdoms of Amalur: Reckoning, Darksiders (Zelda-like structure), Okami HD.
• Puzzle-Dungeon Focus: Lara Croft and the Guardian of Light, DeathSpank.

To play Zelda, you need a Nintendo console. Modern entry points: Breath of the Wild / Tears of the Kingdom (Switch), Ocarina of Time 3D (3DS), Twilight Princess HD (Wii U).