We present optical light curves of 19 radio-quiet (RQ) broad absorption line (BAL) quasi-stellar objects (QSOs) and study their rapid variability characteristics. Systematic CCD observations, aided by a careful data analysis procedure, have allowed us to clearly detect any such microvariability exceeding 0.01–0.02 mag. Our observations cover a total of 13 nights (∼72 h) with each quasar monitored for about 4 h on a given night. Our sample size is a factor of 3 larger than the number of RQ BALQSOs previously searched for microvariability. We introduce a scaled F-test statistic for evaluating the presence of optical microvariability and demonstrate why it is generally preferable to the statistics usually employed for this purpose. Considering only unambiguous detections of microvariability we find that ∼11 per cent of RQ BALQSOs (two out of 19 sources) show microvariability for an individual observation length of about 4 h. This new duty cycle of 11 per cent is similar to the usual low microvariability fraction of normal radio-quiet QSOs (RQQSOs) with observation lengths similar to those of ours. This result provides support for models where RQ BALQSO do not appear to be a special case of the RQQSOs in terms of their microvariability properties.