Integrated positioning and communication (IPAC) system and reconfigurable intelligent surface (RIS) are both considered to be key technologies for future wireless networks. Therefore, in this paper, we propose a RIS-enabled IPAC scheme with the millimeter wave system. First, we derive the explicit expressions of the time-of-arrival (ToA)-based Cramér-Rao bound (CRB) and positioning error bound (PEB) for the RIS-aided system as the positioning metrics. Then, we formulate the IPAC system by jointly optimizing active beamforming in the base station (BS) and passive beamforming in the RIS to minimize the transmit power, while satisfying the communication data rate and PEB constraints. Finally, we propose an efficient two-stage algorithm to solve the optimization problem based on a series of methods such as the exhaustive search and semidefinite relaxation (SDR). Simulation results show that by changing various critical system parameters, the proposed RIS-enabled IPAC system can cater to both reliable data rates and high-precision positioning in different transmission environments.