Cloud Optical Thickness (COT) is a critical cloud property influencing Earth's climate, weather, and radiation budget. Satellite radiance measurements enable global COT retrieval, but challenges like 3D cloud effects, viewing angles, and atmospheric interference must be addressed to ensure accurate estimation. Traditionally, the Independent Pixel Approximation (IPA) method, which treats individual pixels independently, has been used for COT estimation. However, IPA introduces significant bias due to its simplified assumptions. Recently, deep learning-based models have shown improved performance over IPA but lack robustness, as they are sensitive to variations in radiance intensity, distortions, and cloud shadows. These models also introduce substantial errors in COT estimation under different solar and viewing zenith angles. To address these challenges, we propose a novel angle-invariant, attention-based deep model called Cloud-Attention-Net with Angle Coding (CAAC). Our model leverages attention mechanisms and angle embeddings to account for satellite viewing geometry and 3D radiative transfer effects, enabling more accurate retrieval of COT. Additionally, our multi-angle training strategy ensures angle invariance. Through comprehensive experiments, we demonstrate that CAAC significantly outperforms existing state-of-the-art deep learning models, reducing cloud property retrieval errors by at least a factor of nine.