Integrated optical biosensors are gaining increasing attention for their exploitation in lab-on-chip platforms. The standard detection method is based on the measurement of the shift of some optical quantity induced by the immobilization of target molecules at the surface of an integrated optical element upon biomolecular recognition. However, this requires the acquisition of said quantity over the whole hybridization process, which can take hours, during which any external perturbation (e.g., temperature and mechanical instability) can seriously affect the measurement and contribute to a sizeable percentage of invalid tests. Here, we present a different assay concept, named Opto-Magnetic biosensing, allowing us to optically measure off-line (i.e., post hybridization) tiny variations of the effective refractive index seen by microring resonators upon immobilization of magnetic nanoparticles labelling target molecules. Bound magnetic nanoparticles are driven in oscillation by an external AC magnetic field and the corresponding modulation of the microring transfer function, due to the effective refractive index dependence on the position of the particles above the ring, is recorded using a lock-in technique. For a model system of DNA biomolecular recognition we reached a lowest detected concentration on the order of 10 $\mathrm{p}$m, and data analysis shows an expected effective refractive index variation limit of detection of $7.5\times {10}^{-9}$ RIU, in a measurement time of just a few seconds.