Two-point vector-tensor and tensor-tensor correlators of fermionic currents are calculated in a background filled with a constant homogeneous magnetic field. 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.