Is it possible to produce graphene out of air?
A graphene sheet is easily obtained from a block of graphite using adhesive tape. Since graphite itself is essentially a pure grade of coal, it is the result of biological processes in vegetation some millions of years ago. As is pointed out in answers to this Biology.StackExchange question, the majority of a plant's carbon comes from the air via photosynthesis.

So in a sense, we already do that, but we just use the huge stores of graphite from millions of years of high pressure processing beneath our feet rather than start from the beginning.