In the present study, we developed a torque generating machine using an electromagnetic force based on the principle of the Kibble balance method in order to realize a nano-torque traceable to the International System of Units (SI). In order to realize a nano-torque, the size and number of turns of the rectangular coil as well as the magnetic flux density must be reduced. However, when the magnetic flux density is reduced, there is concern about the influence of geomagnetism and other factors. Therefore, we first evaluated the influence of such factors on the machine using a method based on quantum mechanics. As a result, it was found that the influence of geomagnetism on the device is approximately 1 % of the magnetic field formed by the Helmholtz coil at maximum. In addition, the variation of the geomagnetic field during the time of the nano-torque experiment was found to be very small. The torque realized by an electromagnetic force was in the range of approximately 0.2 nN·m to 1 mN·m. Furthermore, the uncertainty in the realized torque was evaluated. Finally, an SI-traceable nano-torque was successfully realized using an electromagnetic force.