Interstellar dust presents a significant challenge to extending parallax-determined distances of optically observed pulsational variables to larger volumes. Distance ladder work at mid- infrared wavebands, where dust effects are negligible and metallicity correlations are minimized, has been largely focused on few-epoch Cepheid studies. Here we present the first determination of mid-infrared period-luminosity (PL) relations of RR Lyrae stars from phase-resolved imaging using the preliminary data release of the Wide-field Infrared Survey Explorer (WISE). We present a novel statistical framework to predict posterior distances of 76 well observed RR Lyrae that uses the optically constructed prior distance moduli while simultaneously imposing a power-law PL relation to WISE- determined mean magnitudes. We find that the absolute magnitude in the bluest WISE filter is M $_W1$ = (- 0.421 ± 0.014) - (1.681 ± 0.147)log$_10$(P/0.50118 day), with no evidence for a correlation with metallicity. Combining the results from the three bluest WISE filters, we find that a typical star in our sample has a distance measurement uncertainty of 0.97% (statistical) plus 1.17% (systematic). We do not fundamentalize the periods of RRc stars to improve their fit to the relations. Taking the Hipparcos-derived mean V-band magnitudes, we use the distance posteriors to determine a new optical metallicity- luminosity relation. The results of this analysis will soon be tested by Hubble Space Telescope parallax measurements and, eventually, with the GAIA astrometric mission.