Abstract. Non-diagonal two-point vector-tensor and tensor-tensor correlator of fermionic currents are calculated in a constant homogeneous magnetic field background. The tensor current is a fermionic part of the Pauli Lagrangian density describing the electromagnetic interaction of fermions through their anomalous magnetic moment (AMM). Under assumption that this interaction enters the effective QED Lagrangian, the contribution induced by AMM to the photon polarization operator is calculated and its impact is discussed.