As stated in the comment by Peter Diehr, the question is in principle no different whether you ask it for electromagnetic, gravitational or any other kind of wave. The wave's entropy is simply the conditional Shannon entropy of the specification needed to define the wave's full state given knowledge of its macroscopically measured variables. A theoretical gravitational wave defined by a full solution of the Einstein Field equations has an entropy of zero just as a full solution of Maxwell's equations does; if you know at the outset that the wave has come from a lone black hole whose state is known, then measurement of the amplitude, polarization and arrival time alone will fully define the wave (the six independent, modulo gauge, components of the metric tensor at your position).
But from these perfectly defined states, gravitational wave and light wave systems can take on "imprints" from their interactions with the World around them in many ways, so that any set of macroscopic measurements of a wave leaves much about the wave's state that is unknown:
As in Lawrence Crowell's Answer, the source could have an unknown configuration. There may be a complicated system of gravitating black holes generating the waves, so our ignorance of this configuration means that we cannot infer the full state of the wave from macroscopic measurements. There could even be some advanced society of creatures modulating the waves for communication purposes; the message that they encode has Shannon entropy that helps compose the wave's total entropy;
Waves scatter from objects; unless the scattering is very simple, the scattering will lead to changes in the full wave state that cannot be gleaned from macroscopic measurements alone. The Optical Grasp of light scattered from rough surfaces increases as properties of the surfaces become encoded into the light's full state which are inaccessible to a macroscopic observer. In theory, gravitational waves are perfectly analogous: their grasp will be increased by interactions with complicated matter systems;
Gravitational waves, like light, can in theory thermalize, so that gravitational black body radiation is in theory possible. One could imagine gravitational waves bouncing back and forth and interacting with vast regions of space filled by black holes and hot gas.
However, I suspect in practice the entropy of gravitational waves will be much lower than that of light. The interaction between gravitational waves and matter is vastly weaker than that between light and matter, simply by dent of (1) the weakness of the gravitational force's action on matter in comparison with that of the electromagnetic force and (2) the fact that gravitational wave sources are quadrupolar and higher order unlike light sources which can be dipolar. Therefore, the thermalization and increase of grasp theorized above are probably just that: theoretical possibilities that seldom if ever arise in our Universe, at least over timescales of the order of the Universe's present age.