Diffusion Tensor Magnetic Resonance Electrical Impedance Tomography (DT-MREIT) is an imaging technique providing low-frequency conductivity tensor images. In all DT-MREIT applications in the literature two linearly independent current injection patterns are used to reconstruct the extra-cellular conductivity and diffusivity ratio (ECDR) which is the space-dependent scale factor between the conductivity and diffusion tensors in a porous medium. In this study, a new approach is proposed to reconstruct ECDR using only one current injection pattern. The proposed method is evaluated using simulated measurements with different SNR levels. The obtained results show similar performance compared to the conventional two current DT-MREIT.