As a kind of wavefront with helical phase, orbital angular momentum (OAM) shows the great potential to enhance the security results of wireless communications due to its unique orthogonality and central hollow electromagnetic wave structure. Therefore, in this paper we propose the reconfigurable-intelligent-surface (RIS) assisted OAM scheme, where RIS is deployed to weaken the information acquisition at eavesdroppers by adjusting the OAM beams pointed to the eavesdropper and artificial noise (AN) is applied to interfere with the eavesdropper, thus significantly increasing the secrecy rates of short-range secure communications. Aiming at obtaining the maximum secrecy rate, we develop the Riemannian manifold conjugate gradient (RMCG) based alternative optimization (AO) algorithm to assign much power to low-order OAM-modes and optimize the OAM beams direction with the programmable RIS, thus respectively enhancing and weakening the received signal strength at the legitimate receiver and the eavesdropper. Numerical results show that our proposed scheme outperforms the existing works in terms of the secrecy rate and the eavesdropper's bit error rate.