We present new empirical infrared period-luminosity-metallicity (PLZ) and period-Wesenheit-metallicity (PWZ) relations for RR Lyae based on the latest Gaia Early Data Release 3 (EDR3) parallaxes. The relations are provided in the Wide-field Infrared Survey Explorer (WISE) W1 and W2 bands, as well as in the W(W1, V - W1) and W(W2, V - W2) Wesenheit magnitudes. The relations are calibrated using a very large sample of Galactic halo field RR Lyrae stars with homogeneous spectroscopic [Fe/H] abundances (over 1000 stars in the W1 band), covering a broad range of metallicities (-2.5 ≲ [Fe/H] ≲ 0.0). We test the performance of our PLZ and PWZ relations by determining the distance moduli of both galactic and extragalactic stellar associations: the Sculptor dwarf spheroidal galaxy in the Local Group (finding ${\bar{\mu }}_{0}=19.47\pm 0.06$ ), the Galactic globular clusters M4 ( ${\bar{\mu }}_{0}=11.16\pm 0.05$ ), and the Reticulum globular cluster in the Large Magellanic Cloud ( ${\bar{\mu }}_{0}=18.23\pm 0.06$ ). The distance moduli determined through all our relations are internally self-consistent (within ≲0.05 mag) but are systematically smaller (by ~2-3σ) than previous literature measurements taken from a variety of methods/anchors. However, a comparison with similar recent RR Lyrae empirical relations anchored with EDR3 likewise shows, to varying extents, a systematically smaller distance modulus for PLZ/PWZ RR Lyrae relations.