We uncover a superconducting state with partial spin polarization induced by a magnetic field. This state, which we call “magnonic superconductor,” lacks a conventional pairing order parameter but is characterized instead by a composite order parameter that represents the binding of electron pairs and magnons. We rigorously demonstrate the existence of magnonic superconductivity with high transition temperature in one-dimensional and two-dimensional Hubbard models with repulsive interaction. We further show that magnonic Cooper pairs can attract to form higher-charge bound states, which can give rise to charge-6 e superconductivity.