We consider dark matter as singlet fermionic particles which carrying magnetic dipole moment to explore its contribution on the polarization of cosmic microwave background (CMB) photons. We show that Dirac fermionic dark matter has no contribution on the CMB polarization. However, in the case of Majorana dark matter this type of interaction leads to the B-mode polarization in presence of primordial scalar perturbations which is in contrast with standard scenario for the CMB polarization. We numerically calculate the B-mode power spectra and plot C BB l for different dark matter masses and the r-parameter. We show that the dark matter with masses less than 100MeV have valuable contribution on C BB l . Meanwhile, the dark matters with mass m d ≤ 50M eV for r = 0.07 ( m d ≤ 80M eV for r = 0.09) can be excluded experimentally. Furthermore, our results put a bound on the magnetic dipole moment about M ≤ 10 −16 e cm in agreement with the other reported constraints.