A method for rapid computation of supersonic rotary derivatives is developed. It is based upon perturbation relation between rotary derivatives and normal velocity on surface due to angular velocity according to Riemann invariant and Euler equations solution using Cartesian meshes. The resulting formula of supersonic rotary derivatives depends only on steady Euler solution of the basic flow, therefore, all supersonic rotary derivatives of interest can be obtained at the same time after obtaining the CFD steady-state Euler solutions. The international dynamic derivatives standard model "Basic Finner" is studied as an example to validate the method. The calculating results are in agreement well with experimental data and reference data appeared in open literature. It is proved that the proposed method has less runtime, higher accuracy and better practicability in engineering, and can be used to rapidly calculate the supersonic rotary derivatives of flying vehicles with complicated configurations due to using Euler solutions of Cartesian meshes.