Monte Carlo simulations are performed to study the effect of an electric field on the surface diffusion of adatoms in a method that measures scanning tunneling microscopy tunneling-current fluctuations. The correlation function of the tunneling-current fluctuations is proportional to the adatom density fluctuation. Diffusion coefficients are inversely proportional to the time constant of the correlation function. Both the shape of the correlation and the measured time constant are calculated as a function of the ratio of the temperature to the characteristic electrostatic energy (i.e., strength of the electric field) and as a function of the initiating time of the measurement. The effect of the field is more pronounced when the measurement is carried out in the early nonequilibrium time regime while the adatom density evolves towards its equilibrium distribution under the spatially dependent electrostatic potential due to the electric field.