The shear viscosity of a variety of strongly interacting quantum fluids, ranging from ultracold atomic Fermi gases to quark-gluon plasmas, can be accurately measured. On the contrary, no experimental data exist, to the best of our knowledge, on the shear viscosity of two-dimensional quantum electron liquids hosted in a solid-state matrix. In this work we propose a Corbino disk device, which allows a determination of the viscosity of a quantum electron liquid from the dc potential difference that arises between the inner and the outer edge of the disk in response to an oscillating magnetic flux.