A definition of degree of coherence of an acoustic wave scattered at a randomly rough surface is given as a special case of the standard form [M. Born and E. Wolf,Principles of Optics(Pergamon, London, 1959), p. 498]. This is accomplished by correlating the signal at a field point scattered by the rough surface and the signal that would be present if the surface were flat. This leads to an interpretation of coherence that is directly associated with the surface.