A broadband dielectric response of ferrofluids can be effectively controlled by application of an external magnetic field. The interaction of magnetic nanoparticles with magnetic forces and the resulting structural changes in the ferrofluids may tune their dielectric spectra. In this paper, we present an experimental study on the controllability of a dielectric spectrum of Mn-Zn ferrite transformer oil-based ferrofluid by means of a static electric field generated by a direct current (DC) bias voltage. Two experimental configurations of the DC bias voltage are applied. The spectrum of a complex permittivity measured in the frequency range from 1 mHz up to 200 kHz is firstly studied under an internal DC bias voltage applied on the electrodes of a measuring capacitor. Then, the sensitivity of the dielectric spectrum to the external DC bias voltage applied on an external pair of electrodes outside the measuring capacitor is investigated. It is found that the increasing internal DC bias voltage significantly shifts the whole dielectric spectrum to lower frequencies and gives rise to higher permittivity values. The external DC bias voltage is remarkably less capable of such tuning. The obtained dielectric spectra are described by a fitting function composed of Havriliak–Negami and conductivity terms. The fitting parameters are compared in the analysis of the two DC bias voltage effects. An interfacial polarization on the nanoparticles is considered to dominate the dielectric spectrum. The aggregation of nanoparticles due to the induced electric polarization and the acting electric forces is discussed as a primary reason of the changes in the dielectric spectra. The DC bias voltage-tunable dielectric spectrum thus complements the controllability of ferrofluids by external forces and may open a new avenue of research and applications in electrical engineering.