  We measure the redshift distribution of a sample of 28 giant arcs discovered
as a part of the Sloan Giant Arcs Survey (SGAS). Gemini/GMOS-North spectroscopy
provides precise redshifts for 24 arcs, and "redshift desert" constraints for
the remaining four. This is a direct measurement of the redshift distribution
of a uniformly selected sample of bright giant arcs, which is an observable
that can be used to inform efforts to predict giant arc statistics. Our primary
giant arc sample has a median redshift z=1.821 and nearly two thirds of the
arcs - 64% - are sources at z \gtrsim 1.4, indicating that the population of
background sources that are strongly lensed into bright giant arcs resides
primarily at high redshift. We also analyze the distribution of redshifts for
19 secondary strongly lensed background sources that are not visually apparent
in SDSS imaging, but were identified in deeper follow-up imaging of the lensing
cluster fields. Our redshift sample for the secondary sources is not
spectroscopically complete, but combining it with our primary giant arc sample
suggests that a large fraction of all background galaxies which are strongly
lensed by foreground clusters reside at z \gtrsim 1.4. Kolmogorov-Smirnov (KS)
tests indicate that our well-selected, spectroscopically complete primary giant
arc redshift sample can be reproduced with a model distribution that is
constructed from a combination of results from studies of strong lensing
clusters in numerical simulations, and observational constraints on the galaxy
luminosity function.
