Switch Loop / End Line Switch - Adding a Ceiling Fan
You can if you’re willing to make the receptacle always hot, in which case you can repurpose the white wire to the switch box as a neutral. Basically, after turning off the power, you remove the switch first. Then, you reconnect the receptacle with your usual middle-of-the-run recertacle wiring, white to silver, black to brass, though you may have to replace the receptacle if it has the tab joining the brass terminals removed. After running new 14/3 cable to the fan from the switch box, simply join the two white wires together. If you want the fan and light controlled independently, you can put in a double switch, one switch controlling the black wire and the other controlling the red.