  We study the propagation effects of radio waves in a pulsar magnetosphere,
composed of relativistic electron-positron pair plasmas streaming along the
magnetic field lines and corotating with the pulsar. We critically examine the
various physical effects that can potentially influence the observed wave
intensity and polarization, including resonant cyclotron absorption, wave mode
coupling due to pulsar rotation, wave propagation through quasi-tangential
regions (where the photon ray is nearly parallel to the magnetic field) and
mode circularization due to the difference in the electron/positron
density/velocity distributions. We numerically integrate the transfer equations
for wave polarization in the rotating magnetosphere, taking account of all the
propagation effects in a self-consistent manner. For typical magnetospheric
plasma parameters produced by pair cascade, we find that the observed radio
intensity and polarization profiles can be strongly modified by the propagation
effects. For relatively large impact parameter (the minimum angle between the
magnetic dipole axis and the line of sight), the polarization angle profile is
similar to the prediction from the Rotating Vector Model, except for a phase
shift and an appreciable circular polarization. For smaller impact parameter,
the linear polarization position angle may exhibit a sudden $90^o$ jump due to
the quasi-tangential propagation effect, accompanied by complex circular
polarization profile. Some applications of our results are discussed, including
the origin of non-gaussion pulse profiles, the relationship between the
position angle profile and circular polarization in conal-double pulsars, and
the orthogonal polarization modes.
