  Many of the observed spin--orbit alignment properties of exoplanets can be
explained in the context of the primordial disk misalignment model, in which an
initially aligned protoplanetary disk is torqued by a distant stellar companion
on a misaligned orbit, resulting in a precessional motion that can lead to
large-amplitude oscillations of the spin--orbit angle. We consider a variant of
this model in which the companion is a giant planet with an orbital radius of a
few au. Guided by the results of published numerical simulations, we model the
dynamical evolution of this system by dividing the disk into inner and outer
parts---separated at the location of the planet---that behave as distinct,
rigid disks. We show that the planet misaligns the inner disk even as the
orientation of the outer disk remains unchanged. In addition to the
oscillations induced by the precessional motion, whose amplitude is larger the
smaller the initial inner-disk-to-planet mass ratio, the spin--orbit angle also
exhibits a secular growth in this case---driven by ongoing mass depletion from
the disk---that becomes significant when the inner disk's angular momentum
drops below that of the planet. Altogether, these two effects can produce
significant misalignment angles for the inner disk, including retrograde
configurations. We discuss these results within the framework of the Stranded
Hot Jupiter scenario and consider their implications, including to the
interpretation of the alignment properties of debris disks.
