The characteristics of nucleation and island growth in oblique angle deposition with substrate rotation have recently attracted interest due to the formation of novel 3D nanostructures by a physical self-assembly process. In this study, we present the results of a solid-on-solid growth simulation by a kinetic Monte Carlo algorithm that explores the layer coverage evolution of thin films during oblique angle deposition. The simulations accounted for oblique incidence flux, shadowing effect, surface diffusion, and substrate rotation. The layer coverage, the ratio of average island volume to average island size, and root-mean-square (RMS) roughness values are reported for the initial stages of island growth from submonolayer thicknesses up to a few monolayers. RMS roughness was also investigated for later stages of the growth. Our results show that, for small deposition angles and with limited or no surface diffusion included, the average growth rate of islands is faster in lateral directions that results in enhanced layer coverages and smoother films. This is due to that the sides of the islands can be exposed to the incident flux more effectively at small deposition angles. On the other hand, normal incidence and high oblique angle depositions give poorer layer coverages and much rougher films due to the slower growth rates in lateral directions.