T cells of the immune system target infected and tumor cells in crowded tissues with high precision by coming into direct contact with the intended target and orienting the intracellular Golgi apparatus and the associated organelles to the area of the cell–cell contact. The mechanism of this orientation remains largely unknown. To further elucidate it we used three-dimensional microscopy of living T cells presented with an artificial substrate mimicking the target cell surface. The data indicate that long, finger-like processes emanate from the T cell surface next to the intracellular Golgi apparatus. These processes come in contact with the substrate and retract. The retraction accompanies the reorientation of the T cell body which brings the Golgi apparatus closer to the stimulatory substrate. Numerical modeling indicates that considering the forces involved the retraction of a process attached with one end to the cell body near the Golgi apparatus and with the other end to the substrate can bring the Golgi apparatus to the substrate by moving the entire cell body. The dynamic scenarios that are predicted by the quantitative model explain features of the reorientation movements that we measured but could not explain previously. We propose that retraction of the surface processes is a force-generating mechanism contributing to the functional orientation of T lymphocytes.