Full-duplex (FD) communication is a promising candidate to address the data rate limitations in underwater acoustic (UWA) channels. Because of transmission at the same time and on the same frequency band, the signal from the local transmitter creates self-interference (SI) that contaminates the the signal from the remote transmitter. At the local receiver, channel state information for both the SI and remote channels is required to remove the SI and equalize the SI-free signal, respectively. However, because of the rapid time-variations of the UWA environment, real-time tracking of the channels is necessary. In this paper, we propose a receiver for UWA-FD communication in which the variations of the SI and remote channels are jointly tracked by using a recursive least squares (RLS) algorithm fed by feedback from the previously detected data symbols. Because of the joint channel estimation, SI cancellation is more successful compared to UWA-FD receivers with separate channel estimators. In addition, due to providing a real-time channel tracking without the need for frequent training sequences, the bandwidth efficiency is preserved in the proposed receiver.