We update the publicly available weak lensing shear measurement algorithm pyRRG for the JWST, and apply it to UNCOVER DR1 imaging of galaxy cluster Abell 2744. At short wavelengths (<2.5 mu m), shear measurements are consistent between independent observations through different JWST bandpasses, and calibrated within 1.5 per cent of those from the Hubble Space Telescope. At longer wavelengths, shear is underestimated by similar to 5 per cent, probably due to coarser pixellization. We model the spatially varying point spread function using WebbPSF, whose moments are within 0.05 of real stars near the centre of the mosaic, where there are sufficient stars to also generate an empirical model. We measure shear from up to 162 galaxies arcmin(-2) to derive a map of dark plus baryonic mass with 12 arcsec (55 kpc) spatial resolution. All code, catalogues, and maps are available from https://github.com/davidharvey1986/pyRRG.