ABSTRACT We present an analysis of the gas dynamics of star-forming galaxies at z ∼ 1.5 using data from the KMOS Galaxy Evolution Survey. We quantify the morphology of the galaxies using HSTcandels imaging parametrically and non-parametrically. We combine the H α dynamics from KMOS with the high-resolution imaging to derive the relation between stellar mass (M*) and stellar specific angular momentum (j*). We show that high-redshift star-forming galaxies at z ∼ 1.5 follow a power-law trend in specific stellar angular momentum with stellar mass similar to that of local late-type galaxies of the form j* ∝ M$_*^{0.53\, ± \, 0.10}$. The highest specific angular momentum galaxies are mostly disc-like, although generally both peculiar morphologies and disc-like systems are found across the sequence of specific angular momentum at a fixed stellar mass. We explore the scatter within the j* – M* plane and its correlation with both the integrated dynamical properties of a galaxy (e.g. velocity dispersion, Toomre Qg, H α star formation rate surface density ΣSFR) and its parametrized rest-frame UV / optical morphology (e.g. Sérsic index, bulge to total ratio, clumpiness, asymmetry, and concentration). We establish that the position in the j* – M* plane is strongly correlated with the star-formation surface density and the clumpiness of the stellar light distribution. Galaxies with peculiar rest-frame UV / optical morphologies have comparable specific angular momentum to disc- dominated galaxies of the same stellar mass, but are clumpier and have higher star formation rate surface densities. We propose that the peculiar morphologies in high-redshift systems are driven by higher star formation rate surface densities and higher gas fractions leading to a more clumpy interstellar medium.