We carry out an exploratory weak gravitational lensing analysis on a combined Very Large Array and Multi-Element Radio-Linked Interferometer Network radio data set: a deep (3.3 μJy beam−1 rms noise) 1.4 GHz image of the Hubble Deep Field-North. We measure the shear estimator distribution at this radio sensitivity for the first time, finding a similar distribution to that of optical shear estimators for Hubble Space Telescope Advanced Camera for Surveys data in this field. We examine the residual systematics in shear estimation for the radio data and give cosmological constraints from radio–optical shear cross-correlation functions. We emphasize the utility of cross-correlating shear estimators from radio and optical data in order to reduce the impact of systematics. Unexpectedly, we find no evidence of correlation between optical and radio intrinsic ellipticities of matched objects; this result improves the properties of optical–radio lensing cross-correlations. We explore the ellipticity distribution of the radio counterparts to optical sources statistically, confirming the lack of correlation; as a result, we suggest a connected statistical approach to radio shear measurements.