We measure the microvortical flows around gold nanorods propelled by ultrasound in water using polystyrene nanoparticles as optical tracers. We infer the rotational frequencies of such nanomotors assuming a hydrodynamic model of this interaction. In this way, we find that nanomotors rotate around their longitudinal axes at frequencies of up to ≈ 2.5 kHz, or ≈ 150 000 rpm, in the planar pressure node of a half-wavelength layered acoustic resonator driven at ≈ 3 MHz with an acoustic energy density of <10 J·m-3. The corresponding tangential speeds of up to ≈ 2.5 mm·s-1 at a nanomotor radius of ≈ 160 nm are 2 orders of magnitude faster than the translational speeds of up to ≈ 20 μm·s-1. We also find that rotation and translation are independent modes of motion within experimental uncertainty. Our study is an important step toward understanding the behavior and fulfilling the potential of this dynamic nanotechnology for hydrodynamically interacting with biological media, as well as other applications involving nanoscale transport, mixing, drilling, assembly, and rheology. Our results also establish the fastest reported rotation of a nanomotor in aqueous solution.