The influence of Rashba effect and Zeeman effect on the properties of bound magnetopolaron in an anisotropic quantum dot are studied with Pekar variational method. The expression of the ground state energy of the bound magnetopolaron is obtained through theoretical derivation. The relationship of the ground state energy of the polaron with the transverse effective confinement length, the longitudinal effective confinement length, the magnetic field cyclotron resonance frequency, and the Coulomb bound potential are discussed, respectively. Owing to the crystal structural inversion asymmetry and the time inversion asymmetry, the polaron energy experiences Rashba spin-orbit splitting and Zeeman splitting. Under the strong and weak magnetic field, we discuss the dominant position of Zeeman effect and Rashba effect, respectively. Owing to the presence of phonons and impurities, the polaron is more stable than the bare electron state.