Isogeometric collocation method (IGC) shows high computational efficiency compared with isogeometric Galerkin method (IGG) when solving partial differential equations (PDEs). However, few studies about IGC have focused on multi-sided physical domains. In this paper, we propose a new IGC method based on toric parameterization (IGCT) for the multi-sided planar physical domains. Due to the high order continuity of toric basis functions, the IGCT method shows more accurate numerical approximation. Moreover, we generalize the adaptive w-refinement method into IGCT (IGCT-w), in which the weights of basis functions in physical domains are optimized independently for geometry representation. The numerical accuracy of IGCT-w is significantly improved by an order of magnitude in comparison with IGCT method. To save the computational cost of IGCT-w, we devise a selection of weights scheme according to relative residuals. Finally, several numerical examples demonstrate the effectiveness and robustness of our proposed method.