  We present a new distance estimation for the Milky Way dwarf spheroidal
satellite Sculptor obtained from multi-epoch mid-infrared observations of RR
Lyrae stars. The 3.6 {\mu}m observations have been acquired with the Infrared
Array Camera on board the Spitzer Space Telescope as part of the SMHASH
Program. Mid-infrared light curves for 42 RRL were obtained, from which we
measured Sculptor's distance modulus to be {\mu} = 19.60 $\pm$ 0.02
(statistical) $\pm$ 0.04 (photometric) mag (with $\sigma_{sys}=$ = 0.09 mag),
using the 3.6 {\mu}m empirical period-luminosity relations derived from the
Galactic globular cluster M4, or {\mu} = 19.57 $\pm$ 0.02 (statistical) $\pm$
0.04 (photometric) mag (with $\sigma_{sys}=$ = 0.11 mag) using empirical
relations in the same passband recently derived from the Large Magellanic Cloud
globular cluster Reticulum. Both these measurements are in good agreement with
values presented in previous works with Sculptor RR Lyrae stars in optical
bands, and are also consistent with recent near-infrared RR Lyrae results. Best
agreement with the literature is found for the latter modulus which is
equivalent to a distance of d = 82 $\pm$ 1 (statistical) $\pm$ 2 (photometric)
kpc (with $\sigma_{sys}=$ = 4 kpc). Finally, using a subsample of RR Lyrae
stars with spectroscopic metallicities, we demonstrate that these distance
estimates are not affected by metallicity effects.
