The Collaborative International Dictionary of English v.0.48:

Carotic \Ca*rot"ic\, a. [Gr. ? stupefying. See Carotid.]
   1. Of or pertaining to stupor; as, a carotic state.
      [1913 Webster]

   2. (Anat.) Carotid; as, the carotic arteries.
      [1913 Webster]