We report an experimental evidence that molecules of anthraquinone dye aggregate in an anisotropic solvent, a nematic liquid crystal (NLC). We observe strong nonlinear dependencies of the dielectric permittivity and anisotropy of light absorption on the dye concentration c. Moreover, the data suggest that the aggregates are linear, but, in contrast to the isotropic case, their formation in a NLC undergoes two different concentration regimes with a well pronounced crossover. These effects are explained by the interplay between the aggregates' lengths and their orientational ordering due to the interaction with the nematic director.