Empowering sensing capabilities is becoming increasingly important in future wireless networks. Meanwhile, intelligent reflecting surface (IRS) and wireless power transfer (WPT) have also received widespread attention as two key technologies to improve network spectrum efficiency and solve device energy shortage issues, respectively. To this end, we investigate an IRS-assisted and WPT-enabled integrated sensing and communication (ISAC) system. Specifically, a base station (BS), with the assistance of the IRS, has the dual functions of radar sensing as well as receiving the data information transmitted by Internet of Things (IoT) devices. IoT devices can charging itself by harvesting the power of radar signals transmitted from the BS. The sensing performance is studied by deriving an exact closed-form expression and an upper bound of the average radar estimation information rate. In addition, we derive an exact expression for the average data information rate to evaluate the communication performance of the system. The simulation results reveal that increasing the number of reflecting elements of the IRS can simultaneously enhance the radar sensing and communication performance.