Point clouds provide rich geometric information about a shape and a deep neural network can be used to learn effective and robust features. In this paper, we propose a novel local feature descriptor, which employs a Siamese network to directly learn robust features from the point clouds. We use a data representation based on the Mercator projection, then we use a Siamese network to map this projection into a 32-dimensional local descriptor. To validate the proposed method, we have compared it with seven state-of-the-art descriptor methods. Experimental results show the superiority of the proposed method compared to existing methods in terms of descriptiveness and robustness against noise and varying mesh resolutions.