  We calculate the gluon Sivers function of the proton in the valence-$x$
region using a light-cone spectator model with the presence of the gluon degree
of freedom. We obtain the values of the parameters by fitting the model
resulting gluon density distribution to the known parametrization. We find that
our results agree with the recent phenomenological extraction of the gluon
Sivers function after considering the evolution effect. We also estimate the
mean transverse momentum of the gluon in a transversely polarized proton and
find that it is within the range implied by the Burkardt sum rule.
