A sample of all radio-quiet quasars or quasars without radio detection taken from the Veron-Cetty - Veron catalog (1993, VERON93, ADC/CDS Cat. VII/166) which were either (i) detected by ROSAT in the ALL-SKY SURVEY (RASS, Voges 1992, in Proc. of the ISY Conference `Space Science', ESA ISY-3, ESA Publications, p.9, ADC/CDS Cat. IX/10), or (ii) detected as targets of pointed observations, or (iii) detected as serendipitous sources in pointed observations that were publicly available in the ROSAT point source catalog (ROSATSRC, Voges et al. 1995, ADC/CDS Cat. IX/11), has been compiled by Yuan et al. (1998, A&A, 330, 108). For all sources, they used the results of the Standard Analysis Software System (SASS, Voges et al. 1992, in Proc. of the ISY Conference `Space Science', ESA ISY-3, ESA Publications, p.223), employing the most recent processing for the Survey data (RASS-II, Voges et al. 1996, ADC/CDS Cat. IX/10). The total number of quasars in this ROSAT Radio-Quiet Quasars Catalog is 846. Sixty-nine of the radio-quiet objects with radio detections have already been presented in a previous paper (Brinkmann, Yuan, and Siebert 1997, Cat. J/A+A/319/413) using the RASS-I results. Seventeen objects were found to be radio-loud from recent radio surveys and were marked in the table. When available, the power law photon indices and the corresponding absorption column densities (NH) were estimated from the two hardness ratios given by the SASS, both with free fitted NH and for Galactic absorption. The unabsorbed X-ray flux densities in the ROSAT band (0.1-2.4keV) were calculated from the count rates using the energy to counts conversion factor for power law spectra and Galactic absorption. The authors used as the photon index the value obtained for the individual source if the estimated 1-{sigma} error was smaller than 0.5, otherwise they used the redshift-dependent mean value (see the paper for details). Notice that the positions of sources in this catalog are not the positions of the X-ray sources, but the optical positions of the quasars as given in the VERON93 Catalog (Wolfgang Brinkmann, 1998 private communication). This database was created by the HEASARC in December 1998, based on CDS/ADC Catalog J/A+A/330/108. This is a service provided by NASA HEASARC .