The connectivity pattern of networks, which are based on a correlation between ground level temperature time series, shows a dominant dense stripe of links in the southern ocean. We show that statistical categorization of these links yields a clear association with the pattern of an atmospheric Rossby wave, one of the major mechanisms associated with the weather system and with planetary scale energy transport. It is shown that alternating densities of negative and positive links (correlations) are arranged in half Rossby wave distances around 3,500 km, 7,000 km and 10,000 km and are aligned with the expected direction of energy flow, distribution of time delays and the seasonality of these waves. It is also shown that long distance links (i.e., of distances larger than 2,000 km) that are associated with Rossby waves are the most dominant in the climate network. Climate networks may thus be used as an efficient new way to detect and analyze Rossby waves, based on reliable and available ground level measurements, in addition to the frequently used 300 hPa reanalysis meridional wind data.