White matter fiber-tracking algorithms have remarkably improved during the last two decades. However, multiple validation studies warn about the reliability and reproducibility of results, and point out to the need for better algorithms. In propagation based tracking, connections are typically modeled as piece-wise linear segments. In this work, we propose a novel propagation based probabilistic tracker using parallel transport frames which is capable of generating geometrically smooth curves. Moreover, our tracker has a mechanism to reduce noise related propagation errors. Our experiments on FiberCup and Human Connectome Project data show visually and quantitatively superior results compared to three algorithms in MRtrix3.