I want to install a ceiling fan with a light in a spare bedroom with no ceiling wiring. What size wire do I need to use to install with cord management channels and plug into an outlet controlled by a switch?
If you want to plug the ceiling fan into an outlet I would say don't. Electrical receptacles are a source of unnecessary resistance. Merely alter the receptacle to a wiremould style box and run the wiremould (through a switch box) to the ceiling fan, making sure you have a good mechanical connection (e.g. wire nuts) within the receptacle/junction box(es). I won't go into cable fill violations here - it's easy enough to parse on the webs. As far as AWG goes - it's easy to determine based on length of run and wattage of aforementioned ceiling fan. It's a safe bet that 14 ga. or larger is sufficient to run any ceiling fan. Individual wires of many gauges are available at most hardware stores in the US. Tim Post's comment above with regard to the single gang extension box and the suitably supported fan-rated box still apply, and should be given more thought than picking the wire gauge.
Good luck with your air movement! Paul