In this work we consider a model including dark sector bosons interacting through tensor currents with Standard Model leptons. We show that for certain values of the interaction constant this model has the potential of providing an explanation for the discrepancy between theory and experiment, regarding the anomalous magnetic moment of the muon. The effect on the already established measurements for the electron are small and the lepton universality violation is naturally incorporated. Possible experimental searches together with systematic approach to characteristic properties of the final states are discussed.