This paper presents a low power microwave oscillator designed as sensor for electron spin resonance (ESR) spectroscopy. Low power consumption is necessary for low temperature operation. Additionally, lower power consumption allows for a lower microwave magnetic field in the sensing volume, which avoids the saturation of samples having long spin relaxation times and, consequently, the degradation of the spin sensitivity. The oscillator operates at 35 GHz, consuming 90 μW at 300 K and 15 μW at 1.4 K. This is the lowest power consumption reported to date for oscillators operating in the same frequency range. The fully integrated oscillator is based on a single HEMT transistor having a gate length of 70 nm and realized using a 2DEG in In0.7Ga0.3As. The chip area is about 0.3 mm^2 . The spin sensitivity is 3×10^8 spins/Hz^(1/2) at 300 K and 1.2×10^7 Spins/Hz^(1/2) at 10 K.