The problem of the kinematic dynamo of a flow generated by inertial waves in a rotating cylinder is addressed using theoretical and numerical approaches. The theoretical approach is based on asymptotic methods in the limit of small viscous and magnetic Ekman numbers, and small inertial wave amplitude. The numerical approach is based on a Galerkin decomposition of the perturbations on the diffusion modes in a cylinder. We consider the case of the spin-over mode, which is a particular stationary inertial wave of azimuthal wavenumber $m=1$ and demonstrate that this inertial wave exhibits dynamo action, if both viscous and magnetic diffusion effects are considered in the analysis. Physical mechanisms responsible of the dynamo as well as scalings for the dynamo growth rate are provided.