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We have made a polarimetric survey of 84 quasi-stellar objects, to supplement published polarization measurements for two samples of quasars identified with flat-spectrum (core-dominant) radio sources in 5 GHz surveys made at Bonn (Kühr 1980) and at the VLA (Perley 1982). The observations were made using the McDonald 2.1m Struve reflector and the polarimeter described by Breger (1979); the typical accuracy is 0.5% for an 18 mag object after half an hour. Earlier surveys, such as those by Stockman, Moore and Angel (1984), included objects of various radio spectral types, and only a small fraction of the objects showed high polarization (> 3%), but our sample of flat-spectrum quasars reveals many more (about half) of the objects to be highly polarized. Some of them are, expectedly, of the BL Lac class, but many of them have strong broad emission lines. There are two striking correlations among the results: