Single-wall carbon nanotubes (SWCNT) are anisotropic nanoparticles that can cause modifications in the electrical and electro-optical properties of liquid crystals. The control of the SWCNT concentration, distribution and reorientation in such self-organized fluids allows for the possibility of tuning the liquid crystal properties. The alignment and reorientation of CNTs are studied in a system where the liquid crystal orientation effect has been isolated. Complementary studies including Raman spectroscopy, microscopic inspection and impedance studies were carried out. The results reveal an ordered reorientation of the CNTs induced by an electric field, which does not alter the orientation of the liquid crystal molecules. Moreover, impedance spectroscopy suggests a nonnegligible anchoring force between the CNTs and the liquid crystal molecules.