We propose a scheme to generate gamma-ray photons with an orbital angular momentum (OAM) and high energy simultaneously from laser-plasma interactions by irradiating a circularly polarized Laguerre-Gaussian laser on a thin plasma target. The spin angular momentum and OAM are first transferred to electrons from the driving laser photons, and then the OAM is transferred to the gamma-ray photons from the electrons through quantum radiation. This scheme has been demonstrated using three-dimensional quantum electrodynamics particle-in-cell simulation. The topological charge, chirality and carrier-envelope phase of the short ultra-intense vortex laser can be revealed according to the pattern feature of the energy density of radiated photons.