We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin s 1/4 0, 1/2, 1, ..., infinity, from which we extract the corresponding classical amplitude to all orders in the spin vector S'`. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-s Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin.