This paper proposes a bargaining game theoretic rate allocation scheme for wireless-powered machine-type communications (MTCs). In the considered body area MTC network (MTCN), a battery-powered user equipment (UE) acting as the MTC gateway (MTCG) is responsible for collecting the information uploaded by in/on body wireless-powered MTC devices (MTCDs). By solving the Nash bargaining solution (NBS) of the proposed cooperative game, the minimum rate requirements of the MTCDs are satisfied. In addition, the network resource can be allocated to the MTCDs in a fair and efficient manner regarding the difference of their channel qualities. In comparison to other traditional resource allocation methods, the simulation results show that the proposed NBS-based method obtains a good tradeoff between the system efficiency and per-node fairness.