This study depicts the influence of the Rashba effect on the band-edge exciton processes in all-inorganic CsPbBr3 perovskite single colloidal nanocrystal (NC). The study is based on magneto-optical measurements carried out at cryogenic temperatures under various magnetic field strengths in which discrete excitonic transitions were detected by linearly and circularly polarized measurements. Interestingly, the experiments show a nonlinear energy splitting between polarized transitions versus magnetic field strength, indicating a crossover between a Rashba effect (at the lowest fields) to a Zeeman effect at fields above 4 T. We postulate that the Rashba effect emanates from a lattice distortion induced by the Cs+motion degree of freedom or due to a surface effect in nanoscale NCs. The unusual magneto-optical properties shown here underscore the importance of the Rashba effect in the implementation of such perovskite materials in various optical and spin-based devices.