We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level—the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.