The mass of the W boson, M_W, plays a central role for high-precision tests of the electroweak theory. Confronting precise theoretical predictions with the accurately measured experimental value provides a high sensitivity to quantum effects of the theory entering via loop contributions. The currently most accurate prediction for the W boson mass in the Minimal R-symmetric Supersymmetric Standard Model (MRSSM) is presented. Employing the on-shell scheme, it combines all numerically relevant contributions that are known in the Standard Model (SM) in a consistent way with all MRSSM one-loop corrections. Special care is taken in the treatment of the triplet scalar vacuum expectation value v_T that enters the prediction for M_W already at lowest order. In the numerical analysis the decoupling properties of the supersymmetric loop contributions and the comparison with the MSSM are investigated. Potentially large numerical effects of the MRSSM-specific Λ superpotential couplings are highlighted. The comparison with existing results in the literature is discussed.