On the basis of the ROSAT All-Sky-Survey, a study of the Taurus-Auriga star forming region has been performed in order to search for hitherto undiscovered T Tauri stars. Our study covers an area of about 280 square degrees, located between 4^h^ and 5^h^ in right ascension and between 15deg and 34deg in declination. Identification of ROSAT All-Sky Survey sources in this area by means of optical spectroscopy revealed 2 new classical T Tauri stars (CTTS) and 66 new weak-line-T Tauri stars (WTTS) with W_{lambda}_(H{alpha})<=10A. Additional pointed ROSAT observations led to the identification of 6 more WTTS and 2 CTTS, giving a total of 76 new T Tauri stars. The large area of our study, as compared with previous works, allows us to study the spatial distribution of WTTS in this star forming region. We find the WTTS of our survey to be distributed over the whole region investigated. There is a noticeable decline of the surface density from south to north within our study area, but the spatial distribution extends most probably beyond our study region. No clustering towards the population of T Tauri stars known prior to ROSAT in Taurus-Auriga could be observed. We suggest that the WTTS found in our study might in part be somewhat older than the previously known T Tauri stars in Taurus-Auriga, and that their broad spatial distribution is due to the typical velocity dispersion of a few km/s measured for Taurus T Tauri stars, in which case for some of our WTTS an age on the order of 10^7^years would be required for reaching the observed distances from the Taurus dark clouds. We estimate a WTTS/CTTS ratio of about 6 within our study area, but conclude that because of the different spatial distribution of WTTS and CTTS this ratio will be most probably significantly larger for a more extended area.