In this paper, we study wireless powered communication networks that employ the slotted ALOHA protocol, which is the preferred protocol for simple and uncoordinated networks. In the energy harvesting (EH) phase, the base station broadcasts radio frequency energy to the EH users (EHUs). The EHUs harvest the broadcasted energy and use it to transmit information back to the base station by contending for access to the uplink channel in the random access (RA) phase. In order to ensure fairness among the users, we propose a proportionally fair resource allocation scheme that exploits the RA nature of slotted ALOHA. Specifically, assuming statistical channel state information, we determine the optimal transmit power at the base station, the optimal durations of the EH and RA phases, the channel access probability, and the rate of each EHU.