This article proposes and analyzes a rotational pressure-correction method for the Navier-Stokes/Darcy (NSD) system with Beavers-Joseph-Saffman-Jones interface conditions. This method mainly solves the Navier-Stokes/Darcy problem in two steps. The first step is the viscous step. The intermediate velocity can be obtained after the pressure gradient is explicitly processed by the algorithm. The second step is the projection step, which first projects the intermediate velocity onto a divergence-free space, and then corrects the velocity and pressure. The main advantage of these methods is that they have first/second order accuracy and do not have the incompressibility constraint of NSD system. For solving the Navier-Stokes equations, each time step requires only one vector-valued elliptic equation and one scalar-valued Poisson equation. Therefore, this method has high computational efficiency. Compared with other traditional related methods, this method is no longer affected by any artificial boundary conditions, and can achieve the optimal convergence order. Finally, unconditional stability and long time stability are established. 2D/3D numerical experiments are presented to illustrate the features of the proposed method and verify the results of the theoretical analysis.