  We have observed the spontaneous appearance of currents in a ring of
ultracold fermionic atoms (6Li) with attractive interactions, following a
quench to a BCS-like pair superfluid. We have measured the winding number
probability distribution for a range of quench rates, with a quench protocol
using simultaneous forced evaporation and interaction ramps to achieve faster
effective quench rates with less atom loss than a purely evaporative quench. We
find that for the fastest quenches the mean square winding number of the
current follows a scaling law in the quench rate with exponent {\sigma} =
0.24(2), which is somewhat lower than that predicted by the Kibble-Zurek
mechanism (KZM) for the three-dimensional XY model (1/3), and unexpectedly
closer to the value obtained from mean-field theory (1/4). For slower quenches
non-universal effects become significant, and we observe a lower rate of
spontaneous current formation that does not follow a simple scaling law.
