  Observations by the Fermi Large Area Telescope of gamma-ray millisecond
pulsar light curves imply copious pair production in their magnetospheres, and
not exclusively in those of younger pulsars. Such pair cascades may be a
primary source of Galactic electrons and positrons, contributing to the
observed enhancement in positron flux above ~10 GeV. Fermi has also uncovered
many new millisecond pulsars, impacting Galactic stellar population models. We
investigate the contribution of Galactic millisecond pulsars to the flux of
terrestrial cosmic-ray electrons and positrons. Our population synthesis code
predicts the source properties of present-day millisecond pulsars. We simulate
their pair spectra invoking an offset-dipole magnetic field. We also consider
positrons and electrons that have been further accelerated to energies of
several TeV by strong intrabinary shocks in black widow and redback systems.
Since millisecond pulsars are not surrounded by pulsar wind nebulae or
supernova shells, we assume that the pairs freely escape and undergo losses
only in the intergalactic medium. We compute the transported pair spectra at
Earth, following their diffusion and energy loss through the Galaxy. The
predicted particle flux increases for non-zero offsets of the magnetic polar
caps. Pair cascades from the magnetospheres of millisecond pulsars are only
modest contributors around a few tens of GeV to the lepton fluxes measured by
AMS-02, PAMELA, and Fermi, after which this component cuts off. The
contribution by black widows and redbacks may, however, reach levels of a few
tens of percent at tens of TeV, depending on model parameters.
