The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle of biological cells. We show that shape oscillations are crucial for local rearrangements that induce ordering of neighboring cells according to their internal clocks even in the absence of signaling and regularization. Our findings reveal a novel, purely physical mechanism through which the internal dynamics of cells influences their collective behavior, which is distinct from well known mechanisms like chemotaxis, cell division, and cell-cell adhesion.