  We compute the far-field time-domain waveform of the gravitational waves
produced in the scattering of two spinning massive objects. The results include
linear-in-spin ($S$) couplings and first-order gravitational corrections
($G^3$), and are valid for encounters in the weak-field regime. Employing a
field-theory framework based on the scattering of massive scalar and vector
particles coupled to Einstein-Hilbert gravity, we derive results for leading
and the next-to-leading spectral waveforms. We provide analytic expressions for
the required scattering data, which include trees, one-loop amplitudes and
their cuts. The expressions are extracted from numerical amplitude evaluations
with the Caravel program, using analytic reconstruction techniques applied in
the classical limit. We confirm a recent prediction for infrared physics of the
classical observable, and observe the surprising appearance of a ultraviolet
singularity, which drops out in the far-field waveform.
