Transmissive and reflective metasurfaces have been extensively studied for generating an orbital angular momentum (OAM)-carrying beam. However, the existing OAM generators suffer from feed blockage, large profile, OAM mode nonreconfigurable, and narrowband. An OAM generator that integrates multiple functions into a single module is in high demand in OAM-based applications. In this study, we proposed an OAM generator based on a folded reflectarray with high-gain low-profile broadband and programmable characteristics. The proposed multifunctional OAM generator, comprising half the volume of the normal OAM metasurfaces, can generate a high-gain l=0, l=+1, and l=+2 OAM-mode-reconfigurable beams with high mode purity over the frequency range of 9.5-10.5 GHz. The proposed OAM generator-integrated multiple functions have potential applications in OAM-based wireless communications and radar detection.