Metasurface-based acoustic vortex generators formed by fixed microstructures can only transfer the first-order orbital angular momentum (OAM) at a single frequency in a waveguide. Here, the multiple order acoustic vortices are realized through a helical metasurface design that is geometrically compact, broadband, and tunable. The proposed metasurface consists of matched helices rotating into the corresponding helical channels, allowing us to modulate the reflected phase shifts of the individual units. The units are arranged in a compact circular configuration and then passively transform an incident plane wavefront into the desired spiral wavefront with a controllable topological charge. The reported theoretical, numerical, and experimental results evidence that multiple orders of OAM modes can be continuously generated by using only a single metasurface. The tunable vortex design is relevant to the pragmatic applications of metasurfaces in real-time acoustic communications, spanners, and tweezers.