  Topological bandstructures interfering with moir\'e superstructures give rise
to a plethora of emergent phenomena, which are pivotal for correlated
insulating and superconducting states of twisttronics materials. While
quasiperiodicity was up to now a notion mostly reserved for solid-state
materials and cold atoms, we here demonstrate the capacity of conventional
superconducting circuits to emulate moir\'e physics in charge space. With two
examples, we show that Hofstadter's butterfly and the magic-angle effect, are
directly visible in spectroscopic transport measurements. Importantly, these
features survive in the presence of harmonic trapping potentials due to
parasitic linear capacitances. Our proposed platform benefits from
unprecedented tuning capabilities, and opens the door to probe incommensurate
physics in virtually any spatial dimension.
