Similar to optical spin-orbit interactions (SOIs), acoustic SOIs are anticipated to offer fresh perspectives and capabilities for acoustic manipulation beyond conventional scalar degrees of freedom. However, the acoustic extrinsic SOIs caused by particular properties of the medium were seldom explored. Here, the acoustic extrinsic SOI is observed in a double spiral acoustic beam (DSAB), as evidenced by the rotation of the spatial intensity pattern along the propagation axis. The interaction of the acoustic plane wave with the well-designed artificial flat structure generates two non-paraxial focused acoustic vortices (NFAVs) with different spin angular momentums. The coaxial coupling between them leads to acoustic spin-controlled orbital rotation (SOR). Theoretical formulations, supported by numerical simulations and experimental results, are provided to demonstrate the validity of acoustic SOR. Our work provides new perspectives and capabilities for understanding sound processing, and may open an avenue for the development of spin-orbit acoustics.