Currently, state-of-the-art methods for 3D object recognition rely in a deep learning-pipeline. Nonetheless, these methods require a large amount of data that is not easy to obtain. In addition to that, the majority of them exploit features of the datasets, like the fact of being CAD models to create rendered representation which will not work in real life because the 3D sensors provide point clouds. We propose a novel global descriptor for point clouds which takes advantage of the fractal dimension of the objects. Our approach introduces many benefits, such as being agnostic to the density of points of the sample, number of points in the input cloud, sensor of choice, and noise up to a level, and it works on real life point cloud data provided by commercial sensors. We tested our descriptor for 3D object recognition using ModelNet, which is a well-known dataset for that task. Our approach achieves 92.84% accuracy on the ModelNet10, and 88.74% accuracy on the ModelNet40.