The morphology of galaxies can be quantified to some degree using a set of scale-invariant parameters. Concentration (C), asymmetry (A), smoothness (S), the Gini index (G), the relative contribution of the brightest pixels to the second-order moment of the flux (M-20), ellipticity (E), and the Gini index of the second-order moment (G(M)) have all been applied to morphologically classify galaxies at various wavelengths. Here, we present a catalog of these parameters for the Spitzer Survey of stellar structure in Galaxies, a volume-limited, near-infrared (NIR) imaging survey of nearby galaxies using the 3.6 and 4.5 mu m channels of the Infrared Array Camera on board the Spitzer Space Telescope. Our goal is to provide a reference catalog of NIR quantified morphology for high-redshift studies and galaxy evolution models with enough detail to resolve stellar mass morphology. We explore where normal, non-interacting galaxies-those typically found on the Hubble tuning fork-lie in this parameter space and show that there is a tight relation between concentration (C-82) and M-20 for normal galaxies. M-20 can be used to classify galaxies into earlier and later types (i.e., to separate spirals from irregulars). Several criteria using these parameters exist to select systems with a disturbed morphology, i.e., those that appear to be undergoing a tidal interaction. We examine the applicability of these criteria to Spitzer NIR imaging. We find that four relations, based on the parameters A and S, G and M-20, G(M), C, and M-20, respectively, select outliers in morphological parameter space, but each selects different subsets of galaxies. Two criteria (G(M) \textgreater 0.6, G \textgreater -0.115 x M-20 + 0.384) seem most appropriate to identify possible mergers and the merger fraction in NIR surveys. We find no strong relation between lopsidedness and most of these morphological parameters, except for a weak dependence of lopsidedness on concentration and M-20.