We present a theoretical study of the electronic structure of a Cd1-yMnyTe quantum dot with Rashba spin-orbit coupling in the presence of a magnetic field. The multiband k(.)p theory is used to describe electrons in Rashba spin-orbit coupling regimes and an external magnetic field, taking into account the sp-d exchange interaction between the carriers and the magnetic ions. We calculated the radius, the thickness, and the magnetic field dependence of Rashba splitting for electrons. We find that the energy levels of electrons for different Mn concentrations exhibit quite different behavior as a function of magnetic field.