We present the results of EVN+MERLIN very long baseline interferometry (VLBI) polarization observations of eight broad absorption line (BAL) quasars at 1.6 GHz, including four low-ionization BAL quasars (LoBALs) and four high-ionization BAL quasars (HiBALs) with either steep or flat spectra on Very Large Array (VLA) scales. Only one steep-spectrum source, J1122+3124, shows two-sided structure on the scale of 2 kpc. The other four steep-spectrum sources and three flat-spectrum sources display either an unresolved image or a core–jet structure on scales of less than 300 pc. In all cases, the marginally resolved core is the dominant radio component. Linear polarization in the cores has been detected in the range of a few to 10 per cent. Polarization, together with high brightness temperatures (from 2 × 109 to 5 × 1010 K), suggests a synchrotron origin for the radio emission. There is no apparent difference in the radio morphologies or polarization between low-ionization and high-ionization BAL quasi-stellar objects (QSOs) or between flat- and steep-spectrum sources. We discuss the orientation of BAL QSOs with both flat and steep spectra, and consider a possible evolutionary scenario for BAL QSOs. In this scenario, BAL QSOs are probably a young population of radio sources that are compact steep spectrum or GHz peaked radio source analogues at the low end of radio power.