A special technique has been developed for producing a composite aerogel which consists of graphene oxide and soy wax (GO/wax). The reduction of graphene oxide was carried out by the stepwise heating of this aerogel to 250 °C. The aerogel obtained in the process of the stepwise thermal treatment of rGO/wax was studied by IR and Raman spectroscopy, scanning electron microscopy, and thermogravimetry. The heat treatment led to an increase in the wax fraction accompanied by an increase in the contact angle of the rGO/wax aerogel surface from 136.2 °C to 142.4 °C. The SEM analysis has shown that the spatial structure of the aerogel was formed by sheets of graphene oxide, while the wax formed rather large (200–1000 nm) clumps in the folds of graphene oxide sheets and small (several nm) deposits on the flat surface of the sheets. The sorption properties of the rGO/wax aerogel were studied with respect to eight solvent, oil, and petroleum products, and it was found that dichlorobenzene (85.8 g/g) and hexane (41.9 g/g) had the maximum and minimum sorption capacities, respectively. In the case of oil and petroleum products, the indicators were in the range of 52–63 g/g. The rGO/wax aerogel was found to be highly resistant to sorption–desorption cycles. The cyclic tests also revealed a swelling effect that occurred differently for different parts of the aerogel.