We have undertaken a near-IR weak-lensing (NIRWL) analysis of the CANDELS HST/WFC3-IR F160W observations. With the Gaia proper motion–corrected catalog as an astrometric reference, we updated the astrometry of the five CANDELS mosaics and achieved an absolute alignment within 002 ± 002, on average, which is a factor of several superior to existing mosaics. These mosaics are available to download (https://drive.google.com/drive/folders/1k9WEV3tBOuRKBlcaTJ0-wTZnUCisS__r). We investigated the systematic effects that need to be corrected for weak-lensing measurements. We find that the largest contributing systematic effect is caused by undersampling. We find a subpixel centroid dependence on the PSF shape that causes the PSF ellipticity and size to vary by up to 0.02 and 3%, respectively. Using the UDS as an example field, we show that undersampling induces a multiplicative shear bias of −0.025. We find that the brighter-fatter effect causes a 2% increase in the size of the PSF and discover a brighter-rounder effect that changes the ellipticity by 0.006. Based on the small range of slopes in a galaxy's spectral energy distribution (SED) within the WFC3-IR bandpasses, we suggest that the impact of the galaxy SED on the PSF is minor. Finally, we model the PSF of WFC3-IR F160W for weak lensing using a principal component analysis. The PSF models account for temporal and spatial variations of the PSF. The PSF corrections result in residual ellipticities and sizes, ∣de1∣ < 0.0005 ± 0.0003, ∣de2∣ < 0.0005 ± 0.0003, and ∣dR∣ < 0.0005 ± 0.0001, that are sufficient for the upcoming NIRWL search for massive overdensities in the five CANDELS fields.