This paper studies a power minimization problem of an orthogonal frequency-division multiplexing modulated two-way amplify-and-forward relay wireless sensor network (WSN). The objective is to develop effective strategies for controlling the transmit power levels of WSN nodes and assigning the bit rates among different subcarriers to minimize the overall transmit power of the network, while ensuring the end-to-end target rates of the two WSN sources. By using channel knowledge at transmitters, a two-step method is proposed to solve the power minimization problem, resulting in a joint power control and bit rate assignment (JPCBRA) algorithm. At the first step, a per-subcarrier optimization problem concerning the power minimization issue is solved, giving closed-form solutions for individual transmit powers at the WSN sources and the relay. At the second step, the end-to-end target rates of the two WSN sources are allocated to different subcarriers so that the total transmit power can be reduced further while satisfying the initial data-rate requirement of the two WSN sources. Computer simulation results confirmed the effectiveness of the proposed JPCBRA algorithm. It is shown that with the JPCBRA algorithm, the total transmit power of the network can be significantly reduced in any traffic and/or channel cases in contrast to the compared schemes.