Globular Clusters (GCs) in the Milky Way are the primary laboratories for establishing the ages of the oldest stellar populations and for measuring the color-magnitude relation of stars. In infrared (IR) color-magnitude diagrams (CMDs), the stellar main sequence (MS) exhibits a kink, due to opacity effects in M dwarfs, such that lower mass and cooler dwarfs become bluer in the IR color baseline. This diagnostic offers a new opportunity to model GC CMDs and to reduce uncertainties on cluster properties (e.g., their derived ages). In this context, we analyzed Hubble Space Telescope Wide Field Camera 3 IR archival observations of four GCs - 47Tuc, M4, NGC2808, and NGC6752 - for which the data are deep enough to fully sample the low-mass MS, reaching at least ~ 2 mag below the kink. We derived the fiducial lines for each cluster and compared them with a grid of isochrones over a large range of parameter space, allowing age, metallicity, distance, and reddening to vary within reasonable selected ranges. The derived ages for the four clusters are respectively 11.6, 11.5, 11.2, and 12.1 Gyr and their random uncertainties are sigma ~ 0.7 - 1.1 Gyr. Our results suggest that the near-IR MS kink, combined with the MS turn-off, provides a valuable tool to measure GC ages and offers a promising opportunity to push the absolute age of GCs to sub-Gyr accuracy with the next generation IR telescopes such as the James Webb Space Telescope and the Wide-Field Infrared Survey Telescope.