Given two graphs, network alignment asks for a potentially partial mapping between the vertices of the two graphs. This arises in many applications where data from different sources need to be integrated. Recent graph aligners use the global structure of input graphs and additional information given for the edges and vertices. We present SINA, an efficient, shared memory parallel implementation of such an aligner. Our experimental evaluations on a 32-core shared memory machine showed that SINA scales well for aligning large real-world graphs: SINA can achieve up to 28.5× speedup, and can reduce the total execution time of a graph alignment problem with 2M vertices and 100M edges from 4.5 hours to under 10 minutes. To the best of our knowledge, SINA is the first parallel aligner that uses global structure and vertex and edge attributes to handle large graphs.