Doctrine and Covenants 89:9 says we shouldn’t drink “hot drinks.” The only official interpretation of this term is the statement made by early Church leaders that it means tea and coffee. Caffeine is not specifically mentioned as the reason not to drink these drinks.
However, we should keep in mind this counsel given by President Boyd K. Packer: “The Word of Wisdom was ‘given for a principle with promise’ (D&C 89:3). … A principle is an enduring truth, a law, a rule you can adopt to guide you in making decisions. Generally principles are not spelled out in detail. Members write in asking if this thing or that is against the Word of Wisdom. … We teach the principle together with the promised blessings. There are many habit-forming, addictive things that one can drink or chew or inhale or inject which injure both body and spirit which are not mentioned in the revelation. … Obedience to counsel will keep you on the safe side of life” (“The Word of Wisdom: The Principle and the Promises,” Ensign, May 1996, 17–18).