The optical absorption of GaAs nanorings (NRs) under a dc electric field and a terahertz (THz) ac electric field applied in the plane containing the NRs is investigated theoretically. The NRs may enclose some magnetic flux in the presence of a magnetic field perpendicular to the NRs plane. Numerical calculation shows that the excitonic effects are essential to correctly describe the optical absorption in NRs. The applied lateral THz electric field, as well as the dc field leads to reduction, broadening and splitting of the exciton peak. In contrast to the presence of a dc field, significant optical absorption peak arises below the zero-field bandgap in the presence of a THz electric field at a certain frequency. The optical absorption spectrum depends evidently on the frequency and amplitude of the applied THz field and on the magnetic flux threading the NRs. This promises potential applications of NRs for magneto-optical and THz electro-optical sensing.