Abstract We present a weak-lensing analysis of the 3 GHz Very Large Array radio survey of the COSMOS field, which we correlate with overlapping Hubble Space Telescope-Advanced Camera for Survey optical observations using both intrinsic galaxy shape and cosmic shear correlation statistics. After cross-matching sources between the two catalogues, we measure the correlations of galaxy position angles and find a Pearson correlation coefficient of 0.14 ± 0.03. This is a marked improvement from previous studies which found very weak, or non-existent correlations, and gives insight into the emission processes of radio and optical galaxies. We also extract power spectra of averaged galaxy ellipticities (the primary observable for cosmic shear) from the two catalogues, and produce optical–optical, radio–optical, and radio–radio spectra. The optical–optical autopower spectrum was measured to a detection significance of 9.80σ and is consistent with previous observations of the same field. For radio spectra (which we do not calibrate, given the unknown nature of their systematics), although we do not detect significant radio–optical (1.50σ) or radio–radio (1.45σ) E-mode power spectra, we do find the E-mode spectra to be more consistent with the shear signal expected from previous studies than with a null signal, and vice versa for B-mode and EB cross-correlation spectra. Our results give promise that future radio weak-lensing surveys with larger source number densities over larger areas will have the capability to measure significant weak-lensing signals.