Yes, Rust Console Edition does support skins. All of our skins are made by our in-house artists at Double Eleven and can be purchased through using Rust Coins.
Rust Coins can be purchased through the platform stores for real money. To use your Rust Coins, you need to visit the Skin Store from the Main Menu, before joining a server.
You can find the Skin Store from the Main Menu > Skin Store.
Skins purchased from the Skin Store will then be allocated to your account, and can be applied to your weapons, armour or tools through using the crafting table in-game.