A synthetic theory of neoclassical and anomalous transport in a weakly turbulent tokamak plasma is presented. The neoclassical effect on the anomalous particle and heat fluxes and the parallel current in the presence of electrostatic fluctuations is investigated using the kinetic equations for the ensemble-averaged and fluctuating distribution functions. It is found in the drift-kinetic and gyro-kinetic orderings for electrons and ions that the Ware pinch components of the anomalous particle and heat fluxes and the parallel current are sensitive to the toroidal effect, although the other components of particle and heat fluxes are little influenced. In the banana regime, these Ware pinch components and the anomalous parallel current are shown to be significantly reduced when the condition [mid ](ω − ωE)/ k∥ve[mid ] < (2ε)1/2 is satisfied, where ω and k∥ are the frequency and the parallel wavenumber of fluctuations, ωE is the drift frequency due to the radial electric field, ve is the thermal velocity for electrons and ε is the inverse aspect ratio. Interpolated formulae that can be used throughout all collisonality regimes are also obtained for the Ware pinch components and the anomalous parallel current.