In a large pitcher, stir together the pineapple juice, rum, lime juice, syrup and the rhubarb slices. Distribute among four ice-filled glasses and serve.
Rhubarb-Ginger syrup: In a small saucepan, combine 3 rhubarb stalks cut into ½-inch slices, 1 2-inch piece of ginger cut into 4 slices, ¾ cup of sugar and ¾ of water. Bring to a boil over medium high heat. Reduce the heat to low and cook until the rhubarb has nearly disintegrated and the ginger has softened, 10-15 minutes. Remove from heat and allow to cool for 5 minutes. Strain the syrup into a bowl and discard the solids.