To complete meiosis II in animal cells, the male DNA material needs to meet the female DNA material contained in the female pronucleus at the egg center, but it is not known how the male pronucleus, deposited by the sperm at the periphery of the cell, finds the cell center in large eggs. Pronucleus centering is an active process that appears to involve microtubules and molecular motors. For small and medium-sized cells, the force required to move the centrosome can arise from either microtubule pushing on the cortex, or cortically-attached dynein pulling on microtubules. However, in large cells, such as the fertilized Xenopus laevis embryo, where microtubules are too long to support pushing forces or they do not reach all boundaries before centrosome centering begins, a different force generating mechanism must exist. Here, we present a centrosome positioning model in which the cytosolic drag experienced by cargoes hauled by cytoplasmic dynein on the sperm aster microtubules can move the centrosome towards the cell’s center. We find that small, fast cargoes (diameter ~100 nm, cargo velocity ~2 mm/s) are sufficient to move the centrosome in the geometry of the Xenopus laevis embryo within the experimentally observed length and time scales.