Colloidal suspensions of anisotropic nanoparticles can spontaneously self-organize in liquid-crystalline phases beyond some concentration threshold. These phases often respond to electric and magnetic fields. At lower concentrations, usual isotropic liquids are observed but they can display very strong Kerr and Cotton-Mouton effects (i.e., field-induced particle orientation). For many examples of these colloidal suspensions, the solvent is water, which hinders most electro-optic applications. Here, for goethite (α-FeOOH) nanorod dispersions, we show that water can be replaced by polar aprotic solvents, such as N-methyl-2-pyrrolidone (NMP) and dimethylsulfoxide (DMSO), without loss of colloidal stability. By polarized-light microscopy, small-angle X-ray scattering and electro-optic measurements, we found that the nematic phase, with its field-response properties, is retained. Moreover, a strong Kerr effect was also observed with isotropic goethite suspensions in these polar aprotic solvents. Furthermore, we found no significant difference in the behavior of both the nematic and isotropic phases between the aqueous and non-aqueous dispersions. Our work shows that goethite nanorod suspensions in polar aprotic solvents, suitable for electro-optic applications, can easily be produced and that they keep all their outstanding properties. It also suggests that this solvent replacement method could be extended to the aqueous colloidal suspensions of other kinds of charged anisotropic nanoparticles.