Pour sugar into a 3-quart saucepan and place over medium-high heat. Cook while stirring gently until the sugar melts and turns golden brown, about 10 minutes.
Carefully and slowly pour in the water, stirring to dissolve the caramel. Add the ginger, lime, and cinnamon; bring to a boil, then reduce heat to medium, and simmer for 10 to 15 minutes. Pour in the cachaca, and cook until hot, about 5 minutes more. Strain before serving.