From the military command of the English Army - where it is still used. The earliest citation that I can find is from Manoeuvres, or Practical observations on the Art of War, 1711, by the English soldier, Major William Young. Young explained the meaning of numerous commands, including:
To the Right Face! - Bring up the firelock, with a quick motion high before you, till your left hand comes even with your eye, with the fingers of your hand extended along the stock, just above the feather spring. The right foot to be brought close up to the left heel in this motion.
To the Right About Face! - As before, coming to the Right About, instead of to the Right.
[About meant 'facing the opposite way']
See also, 'About turn'.