Detecting new states of matter requires new experimental probes. For example, though the quantum spin liquid has been studied theoretically for decades, it remains challenging to identify it in the lab. Measurement of the thermal Hall conductivity has emerged as a promising tool for identifying exotic states of matter, including the spin liquid. However, theinterpretation of these data is complicated by the fact that the transport measurement is agnostic to the type of heat carrier. Additionally, it is difficult to determine from the transport measurement whether the Hall conductivity is intrinsic – a property of bandstructure – or extrinsic – a result of scattering. For this reason, experimental probes with additional specificity are needed to clarify the mechanism of the thermal Hall effect. Here, we develop an experimental technique using pulse echo ultrasound to isolate the intrinsic phonon Hall effect, which is a consequence of phonon Berry curvature, or equivalently, Hall viscosity. In addition to a thermal Hall effect, phonon Hall viscosity results in an acoustic Faraday effect – the time-odd rotation of the polarization of transverse soundwaves. The experimental method presented here measures the acoustic Faraday rotation and is therefore sensitive specifically to the source of intrinsic phonon Hall conductivity. We first test the technique in yttrium iron garnet (YIG), a simple ferrimagnet with known magnetoelastic coupling. Using broadband ultrasonic transducers, we extend existing measurements of the Faraday rotation of YIG over a continuous band of frequencies, strengthening the interpretation of the data in terms of Kittel’s model of coupled magnons and phonons. After confirming the validity of the method, we turn to the spin liquid candidate α-RuCl3. We find non-zero phonon Hall viscosity in α-RuCl3 which peaks near its critical magnetic field, suggesting that the viscosity is the result of coupled spin and lattice degrees of freedom. The Hall viscosity persists above the Neel temperature of α-RuCl3, implying a mechanismdistinct from magnon-phonon hybridization. The value of the Hall viscosity we extract can account for a significant portion of the observed thermal Hall effect, implying that the thermal Hall effect of α-RuCl3 is largely intrinsic, with the transverse heat carried by phonons.