In the early universe, Dirac neutrino magnetic moments due to their chiralityflipping nature could lead to thermal production of right-handed neutrinos, which would make a significant contribution to the effective neutrino number, N eff . We present in this paper a dedicated computation of the neutrino chirality-flipping rate in the thermal plasma. With a careful and consistent treatment of soft scattering and the plasmon effect in finite temperature field theories, we find that neutrino magnetic moments above 3.3 × 10 −12 µ B have been excluded by current CMB and BBN measurements of N eff , assuming three right-handed neutrinos were thermalized. This limit is stronger than the latest bounds from XENONnT and LUX-ZEPLIN experiments and comparable with those from stellar cooling considerations.