A Feshbach resonance occurs when the energy of two interacting free particles comes into resonance with a molecular bound state. When approaching this resonance, marked changes in the interaction strength between the particles can arise. Feshbach resonances provide a powerful tool for controlling the interactions in ultracold atomic gases, which can be switched from repulsive to attractive and have allowed a range of many-body quantum physics effects to be explored. Here we demonstrate a Feshbach resonance based on the polariton spinor interactions in a semiconductor microcavity. By tuning the energy of two polaritons with anti-parallel spins across the biexciton bound state energy, we show an enhancement of attractive interactions and a prompt change to repulsive interactions. A mean-field two-channel model quantitatively reproduces the experimental results. This observation paves the way for a new tool for tuning polariton interactions and to move forward into quantum correlated polariton physics.