It is assumed in the paper that the dominant mechanism for the anomalous electron transport in Tokamaks is the renormalized electron magnetic drift wave driven by temperature gradient. A scaling law for the anomalous electron transport coefficient D(T) has been derived by solving self -consistently the kinetic process, it reads D(T)=(c/ωpe)2 ((ve/qR)2/2π+(vc/2)2)1/2 - vc/2 It coincides in numerical values with the Alcator scaling law given by the Tokamak's experiments, and it agrees with the Ohkawa scaling law in the collisionless limit (vc → 0). Furthermore, its deviation from the Alcator scaling law is analyzed, and the possibility of achieving the thermonuclear ignition for a high-field ohmically heating Tokamak is also discussed based on the scaling law.