In wireless sensor networks (WSNs), utilizing the unmanned aerial vehicle (UAV) as a mobile data collector for the ground sensor nodes (SNs) is an energy-efficient technique to prolong the network lifetime. Specifically, since the UAV can sequentially move close to each of the SNs when collecting data from them and thus reduce the link distance for saving the SNs' transmission energy. In this letter, considering a general fading channel model for the SN-UAV links, we jointly optimize the SNs' wake-up schedule and UAV's trajectory to minimize the maximum energy consumption of all SNs, while ensuring that the required amount of data is collected reliably from each SN. We formulate our design as a mixed-integer non-convex optimization problem. By applying the successive convex optimization technique, an efficient iterative algorithm is proposed to find a sub-optimal solution. Numerical results show that the proposed scheme achieves significant network energy saving as compared to benchmark schemes.