We present results of an electrical impedance spectroscopy investigation of the evolution of the aggregation of methyl orange (MO) in pure aqueous solutions as the concentration of the dye is varied. By applying the constant phase element (CPE) approximation to model the electrical response of the MO solutions, we have verified that the formation of dimers and oligomers can be recognized by specific signatures in the loss and capacitive components of the dielectric response of the system. We interpret these well-defined changes in the dielectric properties of the solutions as a result of molecular rearrangements caused by the aggregation process that alter the current circulation pathways and the electric dipole distribution. The fact that these specific changes in the dielectric behavior coincide with critical concentrations where dimer and oligomer formation in pure aqueous MO solutions are known to occur suggests that electrical impedance spectroscopy can be a competitive technique for the investigation of aggregation behavior in dyes and surfactants.