Ultrasound (US) imaging is widely employed for diagnosis and staging of peripheral vascular diseases (PVD), mainly due to its high availability and the fact it does not emit radiation. However, high inter-operator variability and a lack of repeatability of US image acquisition hinder the implementation of extensive screening programs. To address this challenge, we propose an end-to-end workflow for automatic robotic US screening of tubular structures using only the real-time US imaging feedback. We first train a U-Net for real-time segmentation of the vascular structure from cross-sectional US images. Then, we represent the detected vascular structure as a 3D point cloud and use it to estimate the longitudinal axis of the target tubular structure and its mean radius by solving a constrained non-linear optimization problem. Iterating the previous processes, the US probe is automatically aligned to the orientation normal to the target tubular tissue and adjusted online to center the tracked tissue based on the spatial calibration. The real-time segmentation result is evaluated both on a phantom and in-vivo on brachial arteries of volunteers. In addition, the whole process is validated both in simulation and physical phantoms. The mean absolute radius error and orientation error ($pm$ SD) in the simulation are $1.16pm0.1~mm$ and $2.7pm3.3^{circ}$, respectively. On a gel phantom, these errors are $1.95pm2.02~mm$ and $3.3pm2.4^{circ}$. This shows that the method is able to automatically screen tubular tissues with an optimal probe orientation (i.e. normal to the vessel) and at the same to accurately estimate the mean radius, both in real-time.