We experimentally demonstrate a controlled-not (CNOT) gate with vortex beams carrying orbital angular momentum (OAM) via light storage in a solid driven by electromagnetically induced transparency (EIT). We use vortex beams with different topological charges to perform EIT storage in the double lambda atomic system, the stored information is transferred into a new information channel. The topological charge of the generated signal field is determined by those of the applied fields. The OAM conservation is satisfied in this EIT storage of the double lambda system. By imposing different OAMs into the control and probe fields, we obtain a CNOT gate using EIT storage. This demonstration can be useful for better understanding and developing the OAM applications in the interactions between the OAM and the mediums.