A high sensitive nano superconducting quantum interference device (nanoSQUID) operating as a magnetic flux to critical current transducer with a suitable feedback circuit is employed to measure the magnetization of ferrimagnetic iron oxide nanoparticles. An improved SQUID responsivity has been obtained by using a loop inductance asymmetry. Iron oxide nanoparticles having a mean diameter of 8 nm have been excited by applying a polarizing field in the plane of the nanoSQUID loop. The field dependence of the nanoparticle magnetization at T = 4.2 K shows magnetic hysteresis. Magnetic relaxation measurements are reported and compared with those obtained by using a commercial measurement system.