Tissues use numerous mechanisms to change shape during development. The Drosophila egg chamber is an organ-like structure that elongates to form an elliptical egg. During elongation the follicular epithelial cells undergo a collective migration that causes the egg chamber to rotate within its surrounding basement membrane. Rotation coincides with the formation of a 'molecular corset', in which actin bundles in the epithelium and fibrils in the basement membrane are all aligned perpendicular to the elongation axis. Here we show that rotation plays a critical role in building the actin-based component of the corset. Rotation begins shortly after egg chamber formation and requires lamellipodial protrusions at each follicle cell's leading edge. During early stages, rotation is necessary for tissue-level actin bundle alignment, but it becomes dispensable after the basement membrane is polarized. This work highlights how collective cell migration can be used to build a polarized tissue organization for organ morphogenesis.