In this letter, we investigate the security of a single-antenna rechargeable source node in the presence of a multi-antenna rechargeable cooperative jammer and a potential single-antenna eavesdropper. The batteries at the legitimate transmitting nodes (i.e. the source node and the jamming node) are assumed to be limited in capacity and are modeled as queueing systems. We investigate the impact of the energy arrival rates at the batteries on the achievable secrecy rates. In our energy-constrained network, we propose an efficient scheme to enhance the system's security by optimizing the transmission times of the source node. The jammer uses a subset of its antennas (and transmit radio-frequency chains) to create a beamformer which maximizes the system's secrecy rate while completely canceling the artificial noise at the legitimate destination. Our numerical results demonstrate the significant average secrecy rate gain of our proposed scheme.