In a medium saucepan, bring the granulated sugar and water to a boil over moderately high heat, washing down the side of the pan with a moistened pastry brush. Cook without stirring until a pale-amber caramel forms, about 6 minutes. Remove from the heat and carefully add the red wine. Cook, stirring to dissolve the hardened caramel, until it is slightly reduced, about 3 minutes. Transfer the caramel to a pitcher and serve warm.
The red wine caramel can be refrigerated for up to 1 month. Bring it to room temperature before serving.