The spelling with "t" is the one preferred by the profession itself internationally, but the spelling with "c" is used often enough in texts not written by members of the profession to be considered a valid variant by both American and British dictionaries.
As explained in a 2010 newsletter[REF] of the International Confederation of Dietetic Associations: The correct or preferable spelling of the term "dietitian" has been debated for a long time by dietitians.