We propose a new approach to solve graph isomorphism using parameterized matching. To find isomorphism between two graphs, one graph is linearized, i.e., represented as a graph walk that covers all nodes and edges such that each element is represented by a parameter. Next, we match the graph linearization on the second graph, searching for a bijective function that maps each element of the first graph to an element of the second graph. We develop an efficient linearization algorithm that generates short linearization with an approximation guarantee, and develop a graph matching algorithm. We evaluate our approach experimentally on graphs of different types and sizes, and compare to the performance of VF2, which is a prominent algorithm for graph isomorphism. Our empirical measurements show that graph linearization finds a matching graph faster than VF2 in many cases because of better pruning of the search space.