We present a theoretical and experimental analysis of axisymmetric gravity currents of power-law fluids in homogeneous porous media. The non-Newtonian shear-thinning fluid is a mixture of water, glycerol and Xanthan gum ($n= 0. 33{\unicode{x2013}} 0. 53$), and it is injected into a porous layer of glass beads ($d= 1{\unicode{x2013}} 3~\mathrm{mm} $). We compare experiments conducted with constant ($\alpha = 1$) and time-increasing ($\alpha = 1. 5$ and $2. 0$) influxes to theoretical self-similar solutions obtained by the numerical integration of the nonlinear ordinary differential equation that describes one-dimensional transient motion. The theoretical analysis is confirmed by experimental data. In addition, the selection of the most appropriate expression for the tortuosity factor and the choice of the correct range of shear stress for the determination of the rheological parameters are shown to be crucial to obtaining a good fit between the theory and experiments.