We use a hybrid superconductor-semiconductor transmon device to perform spectroscopy of a quantum dot Josephson junction tuned to be in a spin-1/2 ground state with an unpaired quasiparticle. Because of spin-orbit coupling, we resolve two flux-sensitive branches in the transmon spectrum, depending on the spin of the quasiparticle. A finite magnetic field shifts the two branches in energy, favoring one spin state and resulting in the anomalous Josephson effect. We demonstrate the excitation of the direct spin-flip transition using all-electrical control. Manipulation and control of the spin-flip transition enable the future implementation of charging energy protected Andreev spin qubits.