In recent years, multiple data-driven fiber orientation distribution function (fODF) estimation algorithms and automatic tractography pipelines have been proposed to address the limitations of traditional methods. However, these approaches lack precision and generalizability. To tackle these shortcomings, we introduce CTtrack, a CNN+Transformer-based pipeline to estimate fODFs and perform tractography. In this approach, a convolutional neural network (CNN) module is employed to project the resampled diffusion-weighted magnetic resonance imaging (DW-MRI) data to a lower dimension. Then, a transformer model estimates the fiber orientation distribution functions using the projected data within a local block around each voxel. The proposed model represents the extracted fODFs by spherical harmonics coefficients. The predicted fiber ODFs can be used for both deterministic and probabilistic tractography. Our pipeline was tested in terms of the precision and robustness in estimating fODFs and performing tractography using both simulated and real diffusion data. The Tractometer tool was employed to compare our method with the classical and data-driven tractography approaches. The qualitative and quantitative assessments illustrate the competitive performance of our framework compared to other available algorithms.