  We present a design for a superconducting nanowire binary shift register,
which stores digital states in the form of circulating supercurrents in
high-kinetic-inductance loops. Adjacent superconducting loops are connected
with nanocryotrons, three terminal electrothermal switches, and fed with an
alternating two-phase clock to synchronously transfer the digital state between
the loops. A two-loop serial-input shift register was fabricated with thin-film
NbN and achieved a bit error rate less than $10^{-4}$, operating at a maximum
clock frequency of $83\,\mathrm{MHz}$ and in an out-of-plane magnetic field up
to $6\,\mathrm{mT}$. A shift register based on this technology offers an
integrated solution for low-power readout of superconducting nanowire single
photon detector arrays, and is capable of interfacing directly with
room-temperature electronics and operating unshielded in high magnetic field
environments.
