Both longitudinal and anomalous Hall conductivities are computed in the model of two-dimensional Dirac fermions with a mass in the presence of weak Gaussian spin-independent disorder with an arbitrary correlation function. The anomalous Hall conductivity is shown to be highly sensitive to the correlation properties of the random potential, such as the correlation length, while it remains independent of the integral disorder strength. This property extends beyond the Dirac model making the anomalous Hall effect an interesting tool to probe disorder correlations.