The influence of an external magnetic field on the elastic interelectrode tunneling mediated by a molecular wire is studied theoretically for the case in which the wire contains paramagnetic ions. A spin-filtration effect for incoming electrons and a spin-polarization effect for outgoing electrons can be demonstrated for a wire including a single paramagnetic ion as well as a pair of identical antiferromagnetically coupled ions. It is assumed that each paramagnetic ion reduces its spin in the electronic ground-state from S to S-1/2 if the transferred electron forms an intermediate bound state with the ion. Just such a spin reduction results in a transfer which is spin forbidden for spin-down electrons along the predominant tunneling channels. These channels are characterized by the lowest possible spin-projections of the paramagnetic ions. The spin reduction also determines the magnetic field dependence of the transfer rate in a specific manner. In the case of two paramagnetic ions the combined action of the magnetic field and the exchange interaction between the ions is responsible for a step-like dependence of the tunnel current on the magnetic field. The exact dependence of the interelectrode current on the magnetic field-strength at a low temperature is derived in using Wigner's 6j-symbols methods. The specific spin-polarization effect observed earlier in metal-ferromagnetic insulator-vacuum experiments on electron tunneling is explained in the framework of a spin-filtration effect at which the predominant tunneling channels are responsible for a tunnel interelectrode current.