We study axisymmetric gravity currents consisting of a constant or time-dependent volume of a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lesser density. The intruding fluid is considered to have a pure Ostwald-DeWaele power-law constitutive equation. First, the conditions for buoyancy-viscous balance are examined, and the current rate of spreading is derived with a box-model. An existing self-similar solution to the nonlinear differential problem for the influx of a constant or time-variable volume of fluid is then described. Results from a number of experiments conducted in a 30° sector with shear thinning, Newtonian and shear thickening fluids, and with constant and increasing release rate, are presented and interpreted with the theoretical solution, obtaining globally a very satisfactory agreement. The rheological parameters of the fluid, derived with a best fit procedure, are compared to those measured independently with conventional rheometry. Confidence intervals are evaluated for both estimates of flow behavior and consistency indices. Results support the feasibility of controlled constant flux laboratory experiments with gravity currents in axisymmetric geometry to infer the rheology of power-law fluids, especially at very low shear rates and with shear thinning fluids.