In a medium pot over medium heat, combine orange juice, cranberries, sugar, and cinnamon stick and bring to a boil. Lower heat to medium and heat for a couple of minutes. Remove from heat. Strain liquid into a measuring cup with pouring spout or a small bowl.
Prepare two glasses. Pour about 3 ounces of the cranberry orange simple syrup and tequila over ice in each glass.
Add ginger beer until the glass is almost full.
Squeeze lime juice
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