Context. The study of asteroids, particularly near-Earth asteroids, is key to gaining insights into our Solar System and can help prevent dangerous collisions. Beyond finding new objects, additional observations of known asteroids will improve our knowledge of their orbit. Aims. We have developed an automated pipeline to process and search for asteroid trails in images taken with OmegaCAM, the wide- field imager mounted on the VLT Survey Telescope (VST), on the European Southern Observatory's Cerro Paranal. The pipeline inputs a FITS image and outputs the position, length, and angle of all the asteroids trails detected. Methods. A convolutional neural network was trained on a set of synthetic asteroid trails, with trail lengths 5-120 pixels (1-25″) and S/Ns 3-20. Its performance was tested on synthetic trails and validated using real trails, chosen from the Solar System Object Image Search of the Canadian Astronomy Data Centre. Results. On the synthetic trails, the pipeline achieved a completeness of 70% for trails with length ≥15 pixels (3″), with a precision of 82%. On the real trails, the pipeline achieved a completeness of 65%, with a precision of 44%, a lower value likely due to the higher presence of contaminants and stars in the field. The pipeline was able to detect both low- and high-S/N asteroid trails. Conclusions. Our method shows a strong potential to make new discoveries and precoveries in VST data across the S/N range studied, especially in the fainter end, which remains largely unexplored.