This paper presents the design and implementation of a memristor-based oscillator, investigating potential analog applications for memristors. Inspired from relaxation oscillator operation, the circuit flows a constant current through a memristor in two directions alternately, increasing or decreasing the memristance and the resulting voltage. A following comparator compares the voltage against two thresholds. Switches are then used to control the current direction according to the comparators' output and close the feedback loop for oscillation. Designed and implemented with Winbond 90-nm CMOS and HfO₂-ReRAM technology, measurement results show an operating frequency range of 300 - 1150 kHz, power consumptions of 700 to 830 μW, and κ of <;6.5e-5 for free-running oscillator jitter performance.