  We investigate the effect of the intrinsic spin of a fundamental spinor field
on the surrounding spacetime geometry. We show that despite the lack of a
rotating stress-energy source (and despite claims to the contrary) the
intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect
analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity
where torsion is constrained to be zero. This resolves a paradox regarding the
counter-force needed to restore Newton's third law in the well known spin-orbit
interaction. In addition, the frame-dragging effect gives rise to a {\it
long-range} gravitationally mediated spin-spin dipole interaction coupling the
{\it internal} spins of two sources. We argue that despite the weakness of the
interaction, the spin-spin interaction will dominate over the ordinary inverse
square Newtonian interaction in any process of sufficiently high-energy for
quantum field theoretical effects to be non-negligible.
