  We derive a new twist-3 partonic sum rule for the transverse spin of the
proton, which involves the well-know quark spin structure function
$g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon
polarization density $\Delta G_T(x)$, and quark and gluon canonical orbital
angular momentum densities associated with transverse polarization. This is the
counter part of the sum rule for the longitudinal spin of the proton derived by
Jaffe and Manohar previously. We relate the partonic canonical orbital angular
momentum densities to a new class of twist-3 generalized parton distribution
functions which are potentially measurable in deep-virtual exclusive processes.
We also discuss in detail an important technicality related to the transverse
polarization in the infinite momentum frame, i.e., separation of intrinsic
contributions from the extrinsic ones. We apply our finding to the
transverse-space distributions of partons, angular momentum, and magnetic
moment, respectively, in a transversely polarized proton.
