The non-volatile spin-orbit torque magnetic random access memory (SOT-MRAM) is very attractive memory technology for the nearest future computers because of its various advantages such as non-volatility, high density and scalability. In the present work we propose a model of a graphene recording device for the SOT-MRAM unit cell consisting of a quasi-freestanding graphene intercalated with Au and an ultra-thin Pt layer sandwiched between graphene and a magnetic tunnel junction. As a result of using the claimed graphene recording memory element a faster operation and lower energy consumption will be achieved under the recording information by reducing the electric current required for record. The efficiency of the graphene recording element was confirmed by the experimental results and the theoretical estimations.