We propose a new random access protocol based on reservation ALOHA (R-ALOHA), called ANC-ALOHA, for applying analog network coding (ANC) to the slotted ALOHA channel of satellite networks (SATNETs). Although ANC promises excellent performance in SATNETs, ANC is not guaranteed in slotted ALOHA owing to the inherent randomness. R-ALOHA can be used to acquire a slot for ANC, but there are still two remaining problems to be overcome. First, the reservation maintenance of R-ALOHA does not work for ANC owing to the superposed signals. Second, a channel estimation scheme for ANC is needed in a slotted ALOHA channel. ANC-ALOHA exploits a keep-on sequence as the preamble and postamble of a burst for ANC to solve the above issues. The reduced payload size and delayed transmission are also proposed to assure the reception of the keep-on sequence. We derived an analytic model to verify the throughput of ANC-ALOHA, and validated it based on the simulation results. The results indicate that ANC-ALOHA significantly improves the channel throughput compared to R-ALOHA.