We study the potential employment of improper Gaussian signaling (IGS) in full-duplex relaying (FDR) with non-negligible residual self-interference (RSI) under Nakagami- $m$ fading. IGS is recently shown to outperform traditional proper Gaussian signaling (PGS) in several interference-limited settings. In this paper, IGS is employed as an attempt to alleviate RSI. We use two performance metrics, namely, the outage probability and the ergodic rate. First, we provide upper and lower bounds for the system performance in terms of the relay transmit power and circularity coefficient, a measure of the signal impropriety. Then, we numerically optimize the relay signal parameters based only on the channel statistics to improve the system performance. Based on the analysis, IGS allows FDR to operate even with high RSI. The results show that IGS can leverage higher power budgets to enhance the performance, meanwhile it relieves RSI impact via tuning the signal impropriety. Interestingly, 1-D optimization of the circularity coefficient, with maximum relay power, offers a similar performance as the joint optimization, which reduces the optimization complexity. From a throughput standpoint, it is shown that IGS-FDR can outperform not only PGS-FDR, but also half-duplex relaying with/without maximum ratio combining over certain regions of the target source rate.