Burger King Rodeo Chicken Sandwich Burger King menus, MenusMay 10, 2016Rodeo Chicken Sandwich features deliciously crisp chicken, sweet and smoky BBQ sauce and crispy onion rings served on a toasted sesame seed bun. Burger King Rodeo Burger Burger King menus, MenusJune 15, 2016New Rodeo Burger features a savory flame-grilled beef patty topped with sweet and smoky BBQ sauce and crispy, golden onion rings served on a toasted, sesame seed bun.