Susceptibility tensor imaging (STI) is a magnetic resonance imaging technique that can provide important information for reconstruction of neural fibers and detection of myelination changes in the brain. However, the application of STI in human in vivo has been practically infeasible because of its time-consuming acquisition that requires sampling at multiple (usually more than six) head orientations and the challenging dipole inversion problem involved in image reconstruction. Here, we tackle these issues by presenting a novel image reconstruction algorithm for STI that leverages data-driven priors. Our method, called DeepSTI, learns the data prior implicitly via a deep neural network that resembles the proximal operator of a regularizer function. The dipole inversion problem is then solved iteratively using the learned proximal network. Experimental results demonstrate superior performance of DeepSTI over state-of-the-art methods for STI reconstruction and fiber tractography. DeepSTI is the first to achieve high quality results for in vivo human STI with fewer than six orientations.