We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion-weighted images (DWI), which does not assume a specific diffusion model. We use a recurrent neural network for mapping sequences of DWI values into probabilistic fiber orientation distributions. Based on these estimations, our model facilitates both deterministic and probabilistic streamline tractography. We quantitatively evaluate our method using the Tractometer tool, demonstrating competitive performance with state-of-the-art classical and machine learning based tractography algorithms. We further present qualitative results of bundle-specific probabilistic tractography obtained using our method. The code is publicly available at: https://github.com/itaybenou/DeepTract.git.