Self-assembly of nanoparticles by means of interparticle optical forces provides a compelling approach toward contact-free organization and manipulation of nanoscale entities. However, exploration of the rotational degrees of freedom in this process has remained limited, primarily because of the predominant focus on spherical nanoparticles, for which individual particle orientation cannot be determined. Here, we show that gold nanorods, which self-assemble in water under the influence of circularly polarized light, exhibit synchronized rotational motion at kilohertz frequencies. The synchronization is caused by strong optical interactions and occurs despite the presence of thermal diffusion. Our findings elucidate the intricate dynamics arising from the transfer of photon spin angular momentum to optically bound matter and hold promise for advancing the emerging field of light-driven nanomachinery.