Can I run a single 12 guage wire outside of 12-2 to provide power to a fan?
If the existing wire is the plastic Romex type then you should plan to run another 12-2 with GND wire up to the fan from the switching location. A single insulated conductor is not going to cut the safety mustard. When you run such wire then just common connect the added Neutral and GND wires into those existing connections within the boxes at each end. 

It may actually (in some cases) be easier to simply remove the existing 12-2 connection and replace it with a 12-3 connection.

If your existing wiring is in conduit, flex or other shielded connection scheme according to current jurisdiction requirements then you should be adding the additional or replacement wiring in like form.