No. Iron Golems were added in **Java Edition 1.2.1 (March 2012)** and **Bedrock Edition 0.12.1 (Sept 2015)**.
The **Xbox 360 Edition (TU73 / Title Update 73, Dec 2018 – final update)** is based on an older Bedrock codebase (equivalent to ~0.16/1.0 era) but **Iron Golem spawning was disabled/removed** in the console legacy code branch due to village mechanics differences and performance constraints on the Xenon CPU.
If you play on **Xbox One / Series X|S**, you have the **Bedrock Edition** (same as Switch/PC/Mobile). Iron Golems work fully there. Your Xbox 360 worlds **can be transferred** to Bedrock on Xbox One via the "Sync Old Worlds" button in the main menu (requires Xbox Live).