In this paper, we report the development of a novel technique in which the magnetoresistance of nanostructures is perturbatively measured by transversally modulating the DC magnetic field. It measures the electrical transport counterpart of the transverse magnetic AC-susceptibility. The technique was developed in a conventional four-probe configuration in which a small DC current flows through the sample and a small transverse AC-field perturbates the equilibrium position of the sample magnetization. Lock-in detection, in-phase with the AC-perturbation, is used to measure the voltage signal between the two inner electrodes of the four-probe station. We successfully demonstrated that this signal is proportional to the product of the first derivative of sample resistance with respect to the equilibrium position of the magnetization times the second derivative of the energy with respect to the equilibrium position of the magnetization. These dependences add new features to the technique investigated here that were not captured by the investigations previously reported on the same subject. To show the effective use of the technique, we discuss its application in measuring magnetic properties of thin magnetic films in the non-saturated regime.