We investigate the correlations in galaxy shapes between optical and radio wavelengths using archival observations of the COSMOS field . Cross-correlation studies between different wavebands will become increasingly important for precision cosmology as future large surveys may be dominated by systematic rather than statistical errors . In the case of weak lensing , galaxy shapes must be measured to extraordinary accuracy ( shear systematics of < 0.01 \% ) in order to achieve good constraints on dark energy parameters . By using shape information from overlapping surveys in optical and radio bands , robustness to systematics may be significantly improved without loss of constraining power . Here we use HST-ACS optical data , VLA radio data , and extensive simulations to investigate both our ability to make precision measurements of source shapes from realistic radio data , and to constrain the intrinsic astrophysical scatter between the shapes of galaxies as measured in the optical and radio wavebands . By producing a new image from the VLA-COSMOS L-band radio visibility data that is well suited to galaxy shape measurements , we are able to extract precise measurements of galaxy position angles . Comparing to corresponding measurements from the HST optical image , we set a lower limit on the intrinsic astrophysical scatter in position angles , between the optical and radio bands , of \sigma _ { \alpha } > 0.212 \pi radians ( or 38.2 ^ { \circ } ) at a 95 \% confidence level .