Conventional multiple-input multiple-out (MIMO) technologies have encountered bottlenecks of significantly increasing spectrum efficiencies of wireless communications due to the low degrees of freedom in practical line-of-sight scenarios and severe path loss of high frequency carriers. Orbital angular momentum (OAM) has shown the potential for high spectrum efficiencies in radio frequency domains. To investigate the advantage of OAM in multiuser communications, in this paper we propose the reconfigurable intelligence surface (RIS) assisted OAM multiuser (MU) wireless communication schemes, where RIS is deployed to establish the direct links blocked by obstacles between the OAM transmitter and users, to significantly increase the achievable sum rate (ASR) of MU systems. To maximize the ASR, we develop the alternative optimization algorithm to jointly optimize the transmit power and phase shifts of RIS. The numerical outcomes demonstrate the superiority of our proposed scheme compared to existing methods in terms of ASR.