Inspired by the r-refinement method in isogeometric analysis, in this paper, we propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. We construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information, which is more straightforward and effective. The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee. Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.