In a small saucepan over medium-low heat, combine the brown sugar, water and cinnamon. Cook until all the sugar has dissolved and the mixture is syrupy, 3 to 4 minutes. Remove from the heat and stir in the butter. When melted, vigorously stir in the corn syrup.
Add the softened ice cream to a large bowl. Pour the cinnamon caramel over the ice cream and quickly fold it in; the hot caramel will string as it hits the cold ice cream. Refreeze or serve immediately.