Despite their importance for astrometry and navigation, the active galactic nuclei (AGNs) that comprise the International Celestial Reference Frame (ICRF) are relatively poorly understood, with key information such as their spectroscopic redshifts, AGN spectral type, and emission-/absorption-line properties generally missing from the literature. Using an updated, publicly available, state-of-the-art spectroscopic fitting code optimized for the spectra of AGNs from low to high redshift, we present a catalog of emission-line and spectral continuum parameters for 1014 unique ICRF3 objects with single-fiber spectra from the Sloan Digital Sky Survey DR16. We additionally present black hole virial mass scaling relationships that use H{alpha}-, H{beta}-, MgII-, and CIV-based line widths, all consistent with each other, which can be used in studies of radio-loud objects across a wide range of redshifts, and we use these scaling relationships to provide derived properties such as black hole masses and bolometric luminosities for the catalog. We briefly comment on these properties for the ICRF objects, as well as their overall spectroscopic characteristics.