A quasi-linear theory of the anomalous transport properties of an axisymmetric toroidal plasma caused by unstable drift waves has been developed. Both particle and kinetic energy fluxes across magnetic surfaces are derived and discussed. Applications of the results have been made to several drift instabilities which are likely to be present in actual toroidal devices. Estimates and comparisons for such devices show that the derived anomalous fluxes are likely to be higher than classical values even for small fluctuation levels.