Phase-field damage models have the ability to model crack nucleation, propagation, coalescence and branching in a unified scheme, in contrast to approaches in which the geometrical description of the crack(s) is required. We extend the well-established theory for fracture so that the failure under cyclic loading can be predicted in a finite strain setting, and apply this to rubbers. The model uses the viscous dissipation that is accumulated under cyclic loading as the fatigue damage driving force. A parametric study on the influence of the material parameters for a one-dimensional uniaxial tensile test is presented. From the results, we deduce that the model has the potential to fit experimental data of various rubbers. Subsequently, the extension to 2D is shown with a double edge notch tensile test, where we can observe the crack growth under cyclic loads until total failure.