I believe a hot tub needs to be hard-wired into the panel. The wires also need to be in conduit. So part of the answer is, No, you can't convert an existing outlet.
The remaining question is how to wire it ... I would guess it's a 220 hookup (not sure of that though.)
I would seriously ask an electrician - high voltage + water is not a job for an ameteur. Maybe you could do some of the work, such as laying the conduit & drilling an access hole in the side of the house. Let the electrician do the rest. (It will be worth the money.)