Do I need to run new wire
Option 1, add GFCI protection
Follow this cable back to the house to the service panel.   You want the circuit to start at the service panel, stop at a receptacle inside the house, then go outside.  If it's not like that already, rewire it so it is.   Now install a GFCI receptacle in the indoor location, and feed the outdoor line off the LOAD terminals.
Now install a 3-prong receptacle on the pole, and label it

GFCI Protected
No Equipment Ground

Option 2, retrofit ground
Don't run a whole new 3-wire cable, just run a ground wire.  It does not need to follow the same route.  It does not need to go all the way to the panel, only to any grounded circuit that is also served out of the same panel.  That circuit's ground wire must be at least as large as your ground wire is required to be.
Using the pole won't work.  Ground has two purposes (to wildly oversimplify).  The post would arrest lightning just fine.   However it would fail dismally at returning fault current to the service panel.   Dirt is a poor conductor (that's why they use copper instead).   It wouldn't flow enough current to trip the breaker, and it would just sit there shocking you and anyone between you and the house.  Of course in the latter case, a GFCI will provide that protection.