  In split supersymmetry the gauginos and higgsinos are the only supersymmetric
particles possibly accessible at foreseeable colliders like the CERN Large
Hadron Collider (LHC) and the International Linear Collider (ILC). In order to
account for the cosmic dark matter measured by WMAP, these gauginos and
higgsinos are stringently constrained and could be explored at the colliders
through their direct productions and/or virtual effects in some processes. The
clean environment and high luminosity of the ILC render the virtual effects of
percent level meaningful in unraveling the new physics effects. In this work we
assume split supersymmetry and calculate the virtual effects of the
WMAP-allowed gauginos and higgsinos in Higgs productions e+e- -> Z h and e+e-
-> \nu_e \bar_\nu_e h through WW fusion at the ILC. We find that the production
cross section of e+e- -> Zh can be altered by a few percent in some part of the
WMAP-allowed parameter space, while the correction to the WW-fusion process
e+e- -> \nu_e \bar_\nu_e h is below 1%. Such virtual effects are correlated
with the cross sections of chargino pair productions and can offer
complementary information in probing split supersymmetry at the colliders.
