I read that graphene can be produced by attaching clear tape to graphite and then removing it. This results in a layer of graphene on the tape. If one were to take a very lone strip of clear tape, apply a layer of graphene, roll up the tape, and make suitable connections to wires, could a capacitor be produced?
No, you can't get large continuous sheets of graphene that way. You just get lots of tiny disconnected pieces. If the pieces are not in electrical contact with each other, they won't form a plate that can be used to build a capacitor.
Instead look into the various adhesives that contain graphite, come out clear, and are usually conductive. Everlube has a number of dry film adhesives containing graphite which may be conductive.