Spin qubits in semiconductors are a promising platform for producing highly scalable quantum computing devices. However, it is difficult to realize multiqubit interactions over extended distances. Superconducting spin qubits provide an alternative by encoding a qubit in the spin degree of freedom of an Andreev level. These Andreev spin qubits have an intrinsic spin–supercurrent coupling that enables the use of recent advances in circuit quantum electrodynamics. The first realization of an Andreev spin qubit encoded the qubit in the excited states of a semiconducting weak link, leading to frequent decay out of the computational subspace. Additionally, rapid qubit manipulation was hindered by the need for indirect Raman transitions. Here we use an electrostatically defined quantum dot Josephson junction with large charging energy, which leads to a spin-split doublet ground state. We tune the qubit frequency over a frequency range of 10 GHz using a magnetic field, which also enables us to investigate the qubit performance using direct spin manipulation. An all-electric microwave drive produces Rabi frequencies exceeding 200 MHz. We embed the Andreev spin qubit in a superconducting transmon qubit, demonstrating strong coherent qubit–qubit coupling. These results are a crucial step towards a hybrid architecture that combines the beneficial aspects of both superconducting and semiconductor qubits.