The angular power spectrum of H i 21 cm opacity fluctuations is a useful statistic for quantifying the observed opacity fluctuations as well as for comparing these with theoretical models . We present here the H i 21 cm opacity fluctuation power spectrum towards the supernova remnant Cas A from interferometric data with spacial resolution of 5 \arcsec and spectral resolution of 0.4 km s ^ { -1 } . The power spectrum has been estimated using a simple but robust visibility based technique . We find that the power spectrum is well fit by a power law P _ { \tau } ( U ) = U ^ { \alpha } with a power law index of \alpha \sim - 2.86 \pm 0.10 ( 3 \sigma error ) over the scales of 0.07 - 2.3 pc for the gas in the Perseus spiral arm and 0.002 - 0.07 pc ( 480 - 15730 au ) for that in the Local arm . This estimated power law index is consistent with earlier observational results based on both H i emission over larger scales and absorption studies over a similar range of scales . We do not detect any statistically significant change in the power law index with the velocity width of the frequency channels . This constrains the power law index of the velocity structure function to be \beta = 0.2 \pm 0.6 ( 3 \sigma error ) .