Soak thirteen 8-inch bamboo skewers in water for at least 30 minutes.
Put the tea, rice, and sugar in the center of a sheet of heavy-duty aluminum foil. (If using thinner foil, use 2 or 3 layers.) Fold the foil loosely to form a flat packet.
Prepare a medium-high gas or charcoal grill fire. Clean and oil the grill grate; set aside. Set the tea-smoking packet directly on the hot coals or on top of a metal burner shield. Put the grate back on the grill and close the lid. On a charcoal grill, leave the vents partially open and wait for smoke to rise from the vents. On a gas grill, wait 10 minutes, then open the lid to check for smoke. If there is none, close the lid and check again in a few minutes.
Meanwhile, pat the shrimp dry with paper towels. Thread three shrimp onto each skewer, season with salt, and sprinkle with the cilantro stems.
Arrange the shrimp skewers on the grill grate so they’re not directly over the packet, and then close the lid. Smoke the shrimp, flipping once, until just cooked through, 3 to 5 minutes total. Remove the shrimp from the skewers, cut them in half lengthwise, and set aside.