It has been shown that acoustic waves with helical wavefronts can carry angular momentum, which can be transmitted towards a propagating medium. Such a wave field can be achieved by using a planar array of electroacoustic transducers, forming a given spatial distribution of phased sound sources which produce the desired helical wavefronts. Here, we introduce a technique to generate acoustic vortices, based on the passive acoustic metasurface concept. The proposed metasurface is composed of space-coiled cylindrical unit cells transmitting sound pressure with a controllable phase shift, which are arranged in a discretized circular configuration, and thus passively transforming an incident plane wavefront into the desired helical wavefront. This method presents the advantage of overcoming the restrictions on using many acoustic sources, and it is implemented with a transmitting metasurface which can be easily three-dimensionally printed. The proposed straightforward design principle can be adopted for easy production of acoustic angular momentum with minimum complexity and using a single source.