As part of the data processing for Gaia Data Release~1 (Gaia DR1) a special astrometric solution was computed, the so-called auxiliary quasar solution. This gives positions for selected extragalactic objects, including radio sources in the second realisation of the International Celestial Reference Frame (ICRF2) that have optical counterparts bright enough to be observed with Gaia. A subset of these positions was used to align the positional reference frame of Gaia DR1 with the ICRF2. We describe the properties of the Gaia auxiliary quasar solution for a subset of sources matched to ICRF2, and compare their optical and radio positions at the sub-mas level. Their formal standard errors are better than 0.76~milliarcsec (mas) for 50% of the sources and better than 3.35~mas for 90%. Optical magnitudes are obtained in Gaia's unfiltered photometric G band. The comparison with the radio positions of the defining sources shows no systematic differences larger than a few tenths of a mas. The fraction of questionable solutions, not readily accounted for by the statistics, is less than 6%. Normalised differences have extended tails requiring case-by-case investigations for around 100 sources, but we have not seen any difference indisputably linked to an optical-radio offset in the sources.Read less <