Robot-guided computed tomography enables the inspection of parts that are too large for conventional systems and allows, for instance, the non-destructive and volumetric evaluation of mechanical joining components within already assembled cars in the automotive industry. However, the typical scan time required by such setups is still significant and represents a major barrier for its industrial large-scale application. As an approach to mitigate the necessary time demand, we propose a part-specific adjustment of the acquisition trajectory. Common circular standard trajectories are inherently inefficient, since they are applied independently of the considered inspection task, while the use of acquisition orbits tailored particularly to the investigated object effectively allows a reduction of the required number of projections, which in turn has the potential to directly decrease the scan time significantly. In contrast to former simulation-guided approaches, this work is considered to be the first successful task-specific trajectory optimization being performed on a robot-based industrial CT platform and aims towards providing a first proof of concept that such methods can be practically applied in a shop floor environment. Based on representative results, a reduction of the number of required projections by approx. 55 % or an image quality improvement according to the root-mean squared error by approx. 40 % compared to the conventionally applied planar acquisition trajectory was achieved.