Does wave-particle duality exist for gravitational waves?

Yes. Gravitational waves have been observed, and assuming that quantum mechanics is the right way to think about the universe, then weak gravitational waves of the sort that can be observed at LIGO can be thought of as coherent ensembles of 'graviton' particles.

Now, theoretically this picture is 'OK' because although any quantum field theory that describes gravity is nonrenormalizable, the energy scale at which we expect new physics associated with gravity to be detectable is extremely large ($\sim 10^{19} \text{GeV}$). Hence, we can use an effective theory valid at low energies to describe gravity in terms of particles, even if the 'true' theory of gravity valid at arbitrary energies or length scales is somewhat different conceptually.

Unfortunately, it's impossible with current technology to observe or manipulate single gravitons in a lab, so gravitons are still theoretical.