The anisotropic full waveform inversion (FWI) is a seismic inverse problem for multiple parameters, that aims to simultaneously reconstruct the vertical velocity and the anisotropic parameters of the Earth's subsurface. This multiparameter inverse problem suffers from two issues. First, the objective function of the data fitting is less sensitive to the anisotropic parameters. Second, the crosstalk effect between the different parameters worsens the model update in the iterative inversion. We proposed to statistically regularize the anisotropic FWI using Wasserstein adversarial networks, which penalize the Wasserstein distance between the distribution of the current model parameters and that of the parameters at the borehole locations. The proposed regularizer can mitigate the problems of anisotropic FWI with multiple parameters. Therefore, the method can also be applied to other inverse problems with multiple parameters.