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We investigate the influence of magnons on the temperature dependence and the anisotropy of the spin-orbit torque (SOT). For this purpose, we use third-order perturbation theory in the framework of the Keldysh formalism to derive suitable equations to compute the magnonic SOT. We find several contributions to the magnonic SOT, which depend differently on the spin-wave stiffness A and the temperature T, with the dominating contribution scaling like T2/A2. Based on this formalism, we compute the magnonic SOT in the ferromagnetic Rashba model. For large Rashba parameters, the magnonic SOT is strongly anisotropic, and for small quasiparticle broadening, it may become larger than the nonmagnonic SOT.