[en] We consider dark matter particles as singlet fermionic particles carrying magnetic dipole moment to explore its contribution on the polarization of the cosmic microwave background (CMB) photons. We show that Dirac fermionic dark matter particles have 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 the presence of primordial scalar perturbations which is in contrast with the standard scenario for the CMB polarization. We numerically calculate the B-mode power spectra and plot C${}_l^{BB}$ for different dark matter masses and the r-parameter. We show that dark matter particles with masses less than 100 MeV have a valuable contribution on C${}_l^{BB}$. Meanwhile, dark matter particles with mass m${}_{DM}$ ≤ 50 MeV for r = 0.07 (m${}_{DM}$ ≤ 80 MeV 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.