  Circuit quantum electrodynamics, where photons are coherently coupled to
artificial atoms built with superconducting circuits, has enabled the
investigation and control of macroscopic quantum-mechanical phenomena in
superconductors. Recently, hybrid circuits incorporating semiconducting
nanowires and other electrostatically-gateable elements have provided new
insights into mesoscopic superconductivity. Extending the capabilities of
hybrid flux-based circuits to work in magnetic fields would be especially
useful both as a probe of spin-polarized Andreev bound states and as a possible
platform for topological qubits. The fluxonium is particularly suitable as a
readout circuit for topological qubits due to its unique persistent-current
based eigenstates. In this Letter, we present a magnetic-field compatible
hybrid fluxonium with an electrostatically-tuned semiconducting nanowire as its
non-linear element. We operate the fluxonium in magnetic fields up to 1T and
use it to observe the $\varphi_0$-Josephson effect. This combination of
gate-tunability and field-compatibility opens avenues for the exploration and
control of spin-polarized phenomena using superconducting circuits and enables
the use of the fluxonium as a readout device for topological qubits.
