Inorganic lead-free metal halide perovskites have garnered much attention as low-toxicity alternatives to lead halide perovskites for luminescence and photovoltaic applications. However, the electronic structure and properties of these materials, including the composition dependence of the band structure, spin-orbit coupling, and Zeeman effects, remain poorly understood. Here, we investigated vacancy-ordered Cs3Bi2X9 (X= Cl, Br) perovskite nanocrystals using magnetic circular dichroism spectroscopy. Our results indicate that the excitonic spectra are predominantly composed of direct and indirect band gap transitions and that the Zeeman splitting energy of the direct exciton increases from 0.50 to 0.63 meV at 7 T by substituting Br for Cl. Comparison with analogous results for Cs2AgBiCl6 nanocrystals, obtained by cation substitution, suggests an important effect of charge distribution within electronic bands on the excitonic Zeeman splitting. This work demonstrates that the magneto-optical properties of these materials can be effectively manipulated via chemical composition, suggesting promising applications in photonics, spintronics, and optoelectronics.