  We compute scalar quasinormal mode (QNM) frequencies in rotating black hole
solutions of the most general class of higher-derivative gravity theories, to
quartic order in the curvature, that reduce to General Relativity for weak
fields and are compatible with its symmetries. The wave operator governing the
QNMs is not separable, but we show one can extract the QNM frequencies by a
projection onto the set of spheroidal harmonics. We have obtained accurate
results for the quasinormal frequency corrections relative to Kerr for rotating
black holes with dimensionless spins up to $\sim 0.7$. We also discuss to what
extent our results carry over to the phenomenologically more relevant case of
gravitational QNMs. Finally we provide an ancillary computational package that
allows one to generalize our calculations to any effective energy-momentum
tensor arising from higher-derivative terms in the effective action.
