Soak 4 wooden skewers in water for at least 1 hour. After 1 hour of soaking, preheat a grill to medium heat.
Make the rub: Combine sugar and cardamom in a medium bowl. Mix thoroughly and set aside.
Cut the plums in half and remove the pit. Cut each half into 3 pieces. Place the plum sections on the skewers and then rub the plums with the cardamom sugar.
Place sugared kabobs on grill and cook for 3 to 4 minutes on 1 side; then turn kabobs and grill for an additional 2 to 3 minutes. Remove from the grill and serve warm.