We study the stellar population properties of the IRAC-detected 6 < ~ z < ~ 10 galaxy candidates from the Spitzer UltRa Faint SUrvey Program. Using the Lyman Break selection technique, we find a total of 17 galaxy candidates at 6 < ~ z < ~ 10 from Hubble Space Telescope images (including the full-depth images from the Hubble Frontier Fields program for MACS 1149 and MACS 0717) that have detections at signal-to-noise ratios > or = 3 in at least one of the IRAC 3.6 and 4.5 mum channels. According to the best mass models available for the surveyed galaxy clusters, these IRAC-detected galaxy candidates are magnified by factors of ~1.2-5.5. Due to the magnification of the foreground galaxy clusters, the rest-frame UV absolute magnitudes M sub(1600) are between -21.2 and -18.9 mag, while their intrinsic stellar masses are between 2 x 10 super(8)M sub(middot in circle) and 2.9 x 10 super(9)M sub(middot in circle). We identify two Lyalpha emitters in our sample from the Keck DEIMOS spectra, one at z sub(Lyalpha) = 6.76 (in RXJ 1347) and one at z sub(Lyalpha) = 6.32 (in MACS 0454). We find that 4 out of 17 z > ~ 6 galaxy candidates are favored by z 1 solutions when IRAC fluxes are included in photometric redshift fitting. We also show that IRAC 3.6-4.5 color, when combined with photometric redshift, can be used to identify galaxies which likely have strong nebular emission lines or obscured active galactic nucleus contributions within certain redshift windows.