We have simulated the X-ray polarization data that can be obtained with the Imaging X-ray Polarimetry Explorer, when observing accretion-powered millisecond pulsars. We estimated the necessary exposure times for SAX J1808.4−3658 in order to obtain different accuracy in the measured time-dependent Stokes profiles integrated over all energy channels. We found that the measured relative errors strongly depend on the relative configuration of the observer and the emitting hotspot. The improvement in the minimum relative error in Stokes Q and U parameters as a function of observing time t scales as 1/√t, and it spans the range from 30–90% with a 200 ks exposure time to 20–60% with a 500 ks exposure time (in the case of data binned in 19 phase bins). The simulated data were also used to predict how accurate measurements of the geometrical parameters of the neutron star can be made when modelling only Q and U parameters, but not the flux. We found that the observer inclination and the hotspot co-latitude could be determined with better than 10° accuracy for most of the cases we considered. In addition, we show that the position of a secondary hotspot can also be constrained when the spot is not obscured by an accretion disc. These measurements can be used to further constrain the neutron star mass and radius when combined with modelling of the X-ray pulse profile.