  By following closely Weinberg's soft theorem, which captures the $1/\omega$
pole contribution to the amplitude for soft graviton emissions
($\omega<\Lambda$) on top of an arbitrary background hard process, we calculate
the expectation value of the graviton's angular momentum operator for arbitrary
collisions dressed with soft radiation. We find that the result becomes
independent of the cutoff $\Lambda$ on the graviton's frequency, effectively
localizing at $\omega=0$. In this way, our result captures the contribution to
the angular momentum that comes from the zero-frequency modes. Like the soft
theorem, our formula has an exact dependence on the kinematics of the hard
particles and is only a function of their momenta. As an example, we discuss in
some detail the case of the $2 \to 2$ scattering of spinless particles in
General Relativity and ${\cal N}=8$ supergravity.
