We present light curves and derive periods and amplitudes for a subset of 38 near-Earth objects (NEOs) observed at 4.5 m with the IRAC camera on the the Spitzer Space Telescope, many of them having no previously reported rotation periods. This subset was chosen from about 1800 IRAC NEO observations as having obvious periodicity and significant amplitude. For objects where the period observed did not sample the full rotational period, we derived lower limits to these parameters based on sinusoidal fits. Light curve durations ranged from 42 to 544 minutes, with derived periods from 16 to 270 minutes. We discuss the effects of light curve variations on the thermal modeling used to derive diameters and albedos from Spitzer photometry. We find that both diameters and albedos derived from the light curve maxima and minima agree with our previously published results, even for extreme objects, showing the conservative nature of the thermal model uncertainties. We also evaluate the NEO rotation rates, sizes, and their cohesive strengths.