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Simultaneous wireless information and power transfer (SWIPT) is a promising technology to provide energy and information supplies at the same time in emerging Internet of Things (IoT) systems. In this paper, we focus on leveraging unmanned aerial vehicles (UAVs) to realize energy-transferring and information-transmitting simultaneously in the IoT. This paper investigates the joint optimization of power allocation and trajectory design of the UAV to support infrastructure-starved IoT services. The objective is to maximize the minimum energy harvested among the multiple ground dispersed IoT devices during a finite operating period while guaranteeing the average data rate requirement of each device. Specifically, we study the UAV-assisted SWIPT for the IoT with power splitting, which is mathematically modeled by a variate coupling optimization problem including the UAV's transmit power budget and speed constraint, which is intractable to be directly solved using the existing algorithms. To deal with the problem, this paper develops an efficient iterative algorithm via tactfully constructing the framework of alternating optimization and concave-convex procedure. As a result, it is transformed into settling a series of convex problems. Since the objective function is monotonically increasing and has an upper bound, the convergence can be guaranteed. The simulation results under various parameter configurations indicate our design enhances the efficiency and fairness of power transferred and information transmitted to the IoT devices on the ground over other benchmark schemes.INDEX TERMS Simultaneous wireless information and power transfer, unmanned aerial vehicle, power allocation, trajectory design, power splitting.