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We apply magnetic fields of up to 7 T to an indium arsenide quantum dot (QD) strongly coupled to a photonic crystal cavity. The field lifts the degeneracy of QD exciton spin states, and tune their emission energy by a combination of diamagnetic and Zeeman energy shifts. We use magnetic field tuning to shift the energies of the two exciton spin states to be selectively on resonance with the cavity. Strong coupling between the cavity and both states is observed. Magnetic field tuning enables energy shifts as large as 0.83 meV without significant degradation of the QD-cavity coupling strength.