So you are asking if you can remove the cable from the switch to the light and run a new cable from the switch to the receptacle?

No I was wondering if I could keep everything and run a receptacle off the existing switch. But, I don’t think I can cause there’s no neutral in the switch box

You bring up another issue - no neutral in the switch box. That is now required by code for new installations, I don't know how picky your building inspector, but frequently ANY changes in a circuit requires that that circuit (or, perhaps, the whole house) must be brought up to code. On the other hand, it may be fairly easy to run a new, 3-wire cable to your switch box.