No, a single photon bouncing between two parallel mirrors does not create a gravitational wave. Gravitational waves are generated by accelerating masses or mass distributions that have changing quadrupole moments.
In the case of a single photon bouncing between mirrors, the photon is a massless particle and does not possess mass or create gravitational effects on its own. The motion of a photon between mirrors is described by the laws of classical and quantum electrodynamics, which do not involve gravitational interactions.
Gravitational waves are produced by dynamic processes involving massive objects, such as the motion of massive celestial bodies or astrophysical events like merging black holes or neutron stars. These events generate ripples in the fabric of spacetime, propagating outward as gravitational waves.
While the photon bouncing between mirrors can transfer momentum to the mirrors and create a radiation pressure effect, this effect is related to the electromagnetic interaction between the photon and the mirrors and not gravitational waves.