Transcutaneous spinal cord stimulation (tSCS) is a promising noninvasive alternative to epidural stimulation. However, further studies are needed to clarify how tSCS affects postural control. The aim of this study was to investigate the effect of transcutaneous cervical spinal cord stimulation on postural stability in healthy participants via computerized stabilization. The center of pressure and the frequency spectrum of the statokinesiogram were assessed in 14 healthy volunteers under tSCS conditions with frequencies of 5 Hz or 30 Hz, subthreshold or suprathreshold stimulus strength, open or closed eyes, and hard or soft surfaces in various combinations. The results revealed that not all the changes in the center of the pressure oscillations reached statistical significance when the tSCS was used. However, tSCS at a frequency of 30 Hz with a suprathreshold stimulus strength improved postural stability. The use of subthreshold or suprathreshold tSCS at 5 Hz led to a shift of 60% of the signal power to the low-frequency range, indicating activation of the vestibular system. With tSCS at 30 Hz, the vestibular component remained dominant, but a decrease in the proportion of high-frequency oscillations was observed, which is associated with muscle proprioception. Thus, transcutaneous electrical stimulation of the cervical spinal cord may be an effective method for activating spinal cord neural networks capable of modulating postural control.