The critical current of a percolating superconductor is analyzed in the vicinity of the superconducting transition temperature and near the percolation threshold. The analysis is based on the Landau-Ginzburg formulation and on the self-similar fractal structure of the infinite cluster on a length scale smaller than the connectivity length μp. The penetration depth of the percolating cluster is explicitly taken into consideration. The results are compared with previous theories and with experimental results. The dc paraconductivity above Tc is discussed.