We provide the analytic waveform in time domain for the scattering of two Kerr black holes at leading order in the post-Minkowskian (weak field, but generic velocity) expansion and up to fourth order in both spins. The result is obtained by the generalization of the Kosower-Maybee-O’Connell formalism to radiative observables, combined with the analytic continuation of the five-point scattering amplitude to complex kinematics. We use analyticity arguments to express the waveform directly in terms of the three-point coupling of the graviton to the spinning particles and the gravitational Compton amplitudes, completely bypassing the need to compute and integrate the five-point amplitude. In particular, this allows us to easily include higher-order spin contributions for any spinning compact body. Finally, in the spinless case, we find a new compact and gauge-invariant representation of the Kovacs-Thorne waveform.