Relativistic corrections of order α 2 to the g-factor of H + 2 are calculated with a high accuracy of 9 significant digits for a wide range of rovibrational states. The precision of previous calculations [R. A. Hegstrom, Phys. Rev. A 19, 17 (1979)] is improved by about 5 orders of magnitude by performing nonadiabatic variational calculations and by including recoil corrections. These results allow for non-destructive identification of the internal state through measurement of spin-flip transition frequencies, which is a crucial requirement for proposed spectroscopy experiments on H + 2 and its antimatter counterpartH − 2 in Penning traps [E. G. Myers, Phys. Rev. A 98, 010101(R) (2018)]. Further, they pave the way towards precision calculations of the g-factor through calculation of higher-order QED corrections and hence to an alternative precision route to obtaining the proton-electron mass ratio.