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 Sculptors 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.
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