Distance measures on a coherent scale around the sky are required to address the outstanding cosmological problems of the Hubble Constant and of departures from the mean cosmic flow. The correlation between galaxy luminosities and rotation rates can be used to determine distances to many thousands of galaxies in a wide range of environments potentially out to 200 Mpc. Mid-infrared (3.6 microns) photometry with the Spitzer Space Telescope is particularly valuable as the source of the luminosities because it provides products of uniform quality across the sky. From a perch above the atmosphere, essentially the total magnitude of targets can be registered in exposures of a few minutes. Extinction is minimal and the flux is dominated by the light from old stars which is expected to correlate with the mass of the targets. In spite of the superior photometry, the correlation between mid-infrared luminosities and rotation rates extracted from neutral hydrogen profiles is slightly degraded from the correlation found with I band luminosities. A color correction recovers a correlation that provides comparable accuracy to that available at I band (~20% 1sigma in an individual distance) while retaining the advantages identified above. Without the color correction the relation between linewidth and [3.6] magnitudes is M^{b,i,k,a}_{[3.6]} = -20.34 - 9.74 (log W_{mx}^{i} -2.5). This description is found with a sample of 213 galaxies in 13 clusters that define the slope and 26 galaxies with Cepheid or tip of the red giant branch distances that define the zero point. A color corrected parameter M_{C_{[3.6]}} is constructed that has reduced scatter: M_{C_{[3.6]}} = -20.34 - 9.13 (log W_{mx}^{i} -2.5). Consideration of the 7 calibration clusters beyond 50 Mpc, outside the domain of obvious peculiar velocities, provides a preliminary Hubble Constant estimate of H_0=74+/-5 km/s/Mpc.