The key info is
dedicated branch circuit. This kicks you into §RE3602.12.1. You need to take your 12.6 and divide by 0.80 giving 15.74 amps. Then round it up to 20.
§RE3602.12 Branch circuits serving room air conditioners. A room air conditioner shall be considered as a single motor unit in determining its branch-circuit requirements where all the following conditions are met:
1. It is cord-and attachment plug-connected.
2. The rating is not more than 40 amperes and 250 volts; single phase.
3. Total rated-load current is shown on the room air-conditioner nameplate rather than individual motor currents.
4. The rating of the branch-circuit short-circuit and ground-fault protective device does not exceed the ampacity of the branch-circuit conductors, or the rating of the branch-circuit conductors, or the rating of the receptacle, whichever is less.
§RE3602.12.1 Where no other loads are supplied. The total marked rating of a cord-and attachment plug-connected room air conditioner shall not exceed 80 percent of the rating of a branch circuit where no other appliances are also supplied.
§RE3602.12.2 Where lighting units or other appliances are also supplied. The total marked rating of a cord-and attachment plug-connected room air conditioner shall not exceed 50 percent of the rating of a branch circuit where lighting or other appliances are also supplied.