Advances in resistive random-access memory (ReRAM) show promise to be used in future unconventional computing systems. Voltage-based driving schemes have been normally used both for WRITE and for READ operations on ReRAM cells. An alternative method consists in using only current pulses to drive resistive switching (RS) devices, which has not been thoroughly investigated so far. In this paper, we use a custom circuit of a voltage-controlled low current source to drive self-directed channel RS devices. We measure the voltage on the current-driven devices and calculate its standard deviation. The obtained results showed that its transient response could be exploited for READ operations. With 10-ms wide low current pulses (100nA), there were no errors in several analyses of 215 pseudorandom READ/WRITE events. Moreover, while working with different devices, we found that the high resistive and the low resistive states could be READ with this method, and the average bit error ratio (BER) was 0.075%.