Collective cell migration is a coordinated movement of multi-cell systems essential for various processes throughout life. The collective motions often occur under spatial restrictions, hallmarked by the collective rotation of epithelial cells confined in circular substrates. Here, we aim to explore how geometric shapes of confinement regulate this collective cell movement. We develop quantitative methods for cell velocity orientation analysis, and find that boundary cells exhibit stronger tangential ordering migration than inner cells in circular pattern. Furthermore, decreased tangential ordering movement capability of collective cells in triangular and square patterns are observed, due to the disturbance of cell motion at unsmooth corners of these patterns. On the other hand, the collective cell rotation is slightly affected by a convex defect of the circular pattern, while almost hindered with a concave defect, also resulting from different smoothness features of their boundaries. Numerical simulations employing cell Potts model well reproduce and extend experimental observations. Together, our results highlight the importance of boundary smoothness in the regulation of collective cell tangential ordering migration.