Coat the rabbit with olive oil, inside and out. Season inside and outside with salt, pepper, and roughly diced fresh thyme.
Place the seasoned rabbit in a preheated smoker for two to three hours at a temperature of 225℉. Cook the rabbit in the smoker until the internal temperature reaches 160℉.
Spritz rabbit with apple cider vinegar every 30 minutes during smoking.
Remove the rabbit from the smoker. Let it rest for 5 minutes. Then cut the rabbit into portions and serve.