Azimuthal resistivity surveys are often applied to complement hydrological information or to improve the location of observation boreholes in pump tests. Symmetric electrode configurations cannot distinguish anisotropy from lateral changes or dipping layers, but asymmetric arrays (e.g., the offset Wenner array) can. Tensor radiomagnetotellurics (RMT) is presented as an alternative method in studies of electrical anisotropy in the shallow subsurface. The electromagnetic and geomagnetic transfer functions provide information about the dimensionality of the data. These transfer functions can also be used to find the directions of anisotropy. Data with an anisotropic signature can be inverted for a one‐dimensional (1D) azimuthal anisotropy model. The method is faster than the azimuthal resistivity method. A 380‐m‐long profile of tensor RMT data (12.7–243 kHz) from limestones that overlie shale on the island of Gotland, Sweden, is used to show the merits of the method. The data have a clear anisotropic signature. The data are inverted for a three‐layer 1D model with azimuthal anisotropy using two different approaches: (1) a moving median filter of five neighboring stations and neglecting static shift parameters; and (2) treating each station separately and including static shifts of the electric field in the inversion. Both inversions show models having a marked anisotropy with anisotropy factors of 3.7 and 4.5, respectively, in the limestones. The second approach has a significantly better data fit. However, the first approach is preferred because the models are smoother from station to station.