You cannot play StarCraft II on Xbox 360. It has never been ported to any console.
StarCraft II: Wings of Liberty is Free-to-Play (campaign + ranked multiplayer + co-op commanders up to Lv. 5). Runs on Intel UHD 620 / AMD Vega 8 at 720p Low 30fps. Download via Battle.net.
No workaround brings SC2 to Xbox 360. Play on PC or try Halo Wars 2 on console.