We present a numerical and analytical study of the modifications induced in the collective scattering spectra by the ohmic current governing the equilibrium magnetic configuration in toroidal plasmas. The spectral density function is calculated assuming equilibrium distributions for the (bulk and impurity) ion species and a Spitzer-like distribution to describe the response of the electrons to the applied DC electric field. As expected, the spectral asymmetries can be non-negligibly enhanced in the region of the ion-acoustic frequency. They reach their maxima for tangential scattering geometries, where the magnetic effects on the spectra are negligible. This justifies the assumption of the non-magnetized spectra. The role of the spectral asymmetries in affecting the ion temperature measurements is investigated, and the possibility of inferring the local ohmic current density from the analysis of the low-frequency part of the spectra is verified. The additional effects due to the presence of impurities affecting the spectral shapes are also discussed under realistic conditions. Reference is made to the widely complementary FTU and JET tokamak plasmas, taken as examples of high- and medium-current density regimes, respectively. As a general result, mainly due to the absence of a true ion acoustic resonance in tokamak plasmas (related to a low electron to ion temperature ratio), the peculiarities of the high-current density regimes (high density, low impurity content, etc.) must be met for the current-induced asymmetry in the spectra to become measurable. The ion temperature measurements can be made unaffected by the asymmetries using a simple symmetrization procedure which applies in all cases. In conclusion, a theoretically motivated potential exists for a more detailed experimental investigation of the feasibility of current-density measurements in ohmic plasmas, based on collective scattering.