Originally a military command in the English Army - where it is still used. The earliest citation in print that I can find is from A Plan of Discipline, Composed for the Use of the Militia, by William Windham and George Townshend, 1760:
When he [the commanding officer] would have them [the battalion] retreat, he either gives the words of command,
To the right about! Turn!
or else orders the drummers to beat the Retreat.
'Turn about' was a common colloquial phrase prior to this, meaning simply 'turn to face the opposite direction'.
See also, 'About face'.