We study theoretical X-ray light curves and polarization properties of accretion-powered millisecond pulsars. We assume that the radiation is produced in two antipodal spots at the neutron star surface which are associated with the magnetic poles. We compute the angle-dependent intensity and polarization produced in an electron-scattering dominated plane-parallel accretion shock in the frame of the shock. The observed flux, polarization degree and polarization angle are calculated accounting for special and general relativistic effects. The calculations also extended to the case of nuclear-powered millisecond pulsars -- X-ray bursts. In this case, we consider one spot and the radiation is assumed to be produced in the atmosphere of the infinite Thomson optical depth. The light curves and polarization profiles show a large diversity depending on the model parameters. Presented results can be used as a first step to understand the observed pulse profiles of accretion- and nuclear-powered millisecond pulsars. Future observations of the X-ray polarization will provide a valuable tool to test the geometry of the emission region and its physical characteristics.
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