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Flexible antennas have attracted great interest due to the variety of areas of their practical use. Here we propose a design of a flexible antenna for generating electromagnetic waves carrying orbital angular momentum (OAM). The ANSYS HFSS electromagnetic solver is used for fullwave numerical simulations targeted to obtain suitable antenna parameters. A prototype of the graphene-based antenna for operating in the microwave range is manufactured and tested. The obtained experimental results confirm the possibility of the proposed antenna with a curved surface to stably generate waves carrying OAM.