  We investigate the issue of whether quasiparticles in the fractional quantum
Hall effect possess a fractional intrinsic spin. The presence of such a spin
$S$ is suggested by the spin-statistics relation $S=\theta/2\pi$, with $\theta$
being the statistical angle, and, on a sphere, is required for consistent
quantization of one or more quasiparticles. By performing Berry-phase
calculations for quasiparticles on a sphere we find that there are two terms,
of different origin, that couple to the curvature and can be interpreted as
parts of the quasiparticle spin. One, due to self-interaction, has the same
value for both the quasihole and quasielectron, and fulfills the
spin-statistics relation. The other is a kinematical effect and has opposite
signs for the quasihole and quasielectron. The total spin thus agrees with a
generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = \theta/2\pi$. On the
plane, we do not find any corresponding terms.
