We study a fully classical covariant relativistic plasma theory including the effect of the spin in the radiation reaction effects of charged particles inmersed in inhomogeneous electromagnetic fields.We include the effect of the radiation reaction due to dynamical spin. We calculate the contribution of the spin-electromagnetic coupling in the radiation reaction for an accelerated particle, in the same fashion than classical radiation reaction owing to its charge.We also obtain the contribution of the radiation reaction to the evolution of the spin dynamics.