Graph matching, which aims to establish correspondences between two geometrical graphs, is a general and powerful tool for pattern recognition and computer vision. However, many factors degrade the matching accuracy. The graph structure suffering from deformation and rotation variations is a key issue in the process of matching. In this work, we propose a joint framework in the reproducing kernel Hilbert space (RKHS) for graph matching with deformation and rotation variations, which incorporates the kernelized unary alignment and local structure alignment into a joint framework. Specifically, the proposed method is able to enhance the node to node correspondence and the edge to edge correspondence and avoids the effect of deformation and rotation by maximizing the similarities between the source graph and the transformed target graph in the reproducing kernel Hilbert space. Meanwhile, an effective algorithm is presented to solve the joint framework. Comprehensive discussion, involving convergence analysis and parameter sensitive analysis, are as well proposed. Promising experimental results in the variety of graph matching tasks such as deformation and rotation are provided to evidence the superiority of the proposed method.