A constraint on the rheology of oceanic mantle is derived on the basis of a recently established scaling law for the onset of convection with temperature-dependent viscosity. Our approach is free from the assumption of statistically steady-state convection, which has commonly been employed in previous studies. The estimated range of asthenospheric viscosity is 1--4 ¿ 1019 Pa s if the activation energy is 300 kJ mol-1, and 4 ¿ 1019-- 1020 Pa s if the activation energy is 100 kJ mol-1. The former range is consistent with laboratory data as well as geodynamic inference based on the geoid. The latter is consistent with geodynamic inference based on seamount loading history. Different activation energies predict different temperature contrasts in convecting mantle. Seismic tomography has the potential to discriminate between these possibilities.