© 2015 American Physical Society. We examine the physics of the early universe when Majorana neutrinos (νe, νμ, ντ) possess transition magnetic moments. These extra couplings beyond the usual weak interaction couplings alter the way neutrinos decouple from the plasma of electrons/positrons and photons. We calculate how transition magnetic moment couplings modify neutrino decoupling temperatures, and then use a full weak, strong, and electromagnetic reaction network to compute corresponding changes in big bang nucleosynthesis abundance yields. We find that light element abundances and other cosmological parameters are sensitive to magnetic couplings on the order of 10-10μB. Given the recent analysis of sub-MeV Borexino data which constrains Majorana moments to the order of 10-11μB or less, we find that changes in cosmological parameters from magnetic contributions to neutrino decoupling temperatures are below the level of upcoming precision observations.