The thermopower of Si nanowires was investigated on the basis of electronic transport theory, taking into account ionized impurity scattering as well as electron-phonon scattering. It was found that the enhancement of the Seebeck coefficient in nanowires arising from quantum confinement is unimportant due to the ionized impurity scattering associated with donor deactivation. Furthermore, because the electrical conductivity is degraded significantly as the nanowire size becomes smaller, despite the accompanying slightly enhanced Seebeck coefficient, the reduction of the nanowire size is not beneficial, at least for the thermopower of devices.