In this paper, we propose a filter-and-forward relay scheme with energy harvesting for single-carrier transmission in frequency-selective channels. The relay node harvests energy from both the source node transmit signal and its own transmit signal by self-energy recycling. The signal received by the relay node is filtered to suppress the inter-symbol interference and then forwarded to the destination node using the harvested energy. We consider a filter design method based on the signal-to-interference-plus-noise power ratio maximization, subject to a constraint that limits the relay transmit power. In addition, we provide a golden-section search based algorithm to optimize the power splitting ratio of the power splitting protocol. The simulation results show that filtering and self-energy recycling of the proposed scheme are effective in improving performance. It is also shown that the proposed scheme is useful even when only partial channel state information is available.