It is increasingly recognized that the investigation of the rotational motion of geometric nanoparticles in the cellular internalization process is significant to understand certain fundamental cellular activities, such as endocytosis. However, the mechanism of rotation of geometric nanoparticles in the internalization process is still largely unknown. Here, we investigate the rotational dynamics of geometric nanoparticles when they adhere onto or are wrapped by lipid membranes, by using dissipative particle dynamics. A variety of rotational modes of the nanoparticles are observed, which are closely related to the complicated competition in the internalization process. We find that the breaking of geometric symmetry of a nanoparticle is important for the occurrence of particle rotation, while its effect can be changed by the orientation of the nanoparticles and the affinity between the ligands and the receptors. Importantly, it is found by our simulations that the rotational mode even determines the possible perturbation of the geometric nanoparticle to the membrane and the configuration between the nanoparticle and lipid membrane in the internalization process. These results provide a new strategy and also provide pivotal insight for the design of nanoparticles as advanced drug-delivery vectors to cells.