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In easy-plane magnets, the spin superfluid phase was predicted to facilitate coherent spin transport. So far, experimental evidence remains elusive. In this Letter, we propose an indirect way to sense this effect via the spin superfluid quantum interference device (spin SQUID), inspired by its superconducting counterpart (rf SQUID). The spin SQUID is constructed as a quasi-one-dimensional (1D) magnetic ring with a single Josephson weak link, functioning as an isolated device with a microwave response. The spin current is controlled by an in-plane electric field through Dzyaloshinskii-Moriya interaction. This interaction can be interpreted as a gauge field that couples to the spin supercurrent through the Aharonov-Casher effect. By investigating the static and dynamic properties of the device, we show that the spin current and the harmonic frequencies of the spin superfluid are periodic with respect to the accumulated Aharonov-Casher phase and are, therefore, sensitive to the radial electric flux through the ring in units of an electric flux quantum, suggesting a potential electric-field sensing functionality. For readout, we propose to apply spectroscopic analysis to detect the frequency shift of the harmonic modes induced by this magnonic Stark effect.