The ultra-reliable and low-latency communication (URLLC) systems are expected to support the stringent quality of service (QoS) demands in the Internet of Things (IoT) networks. In order to support the strict latency and reliability constraints, it is preferable to deploy a reconfigurable intelligent surface (RIS) in the URLLC systems to improve the link quality. In this paper, we focus on the uplink of an RIS-assisted URLLC system, and we propose to minimize the transmission latency under the reliability constraints. To solve the non-convex problem, a low-complexity algorithm is proposed by using the Alternating Direction Method of Multipliers (ADMM) technique. The RIS phase shifts optimization, which is typically non-convex, is efficiently solved by formulating as a Quadratically Constrained Quadratic Programming (QCQP) problem. Simulation results verify that our proposed ADMM-based method is able to achieve better performance than the conventional semi-definite relaxation (SDR)-based method with lower computational complexity. Our proposed RIS-assisted URLLC system is able to significantly reduce the transmission latency, which highlights the great potential in deploying RIS in the IoT networks with strict reliability requirements.