Approx. How much would it cost to put in a 220 v. outlet?

Well are you talking DIY or for an electrician?

Are you asking how much to just install the outlet or is the prep work: Sizing the load, Sizing the conductors and the length of the run, is it allowed by code, Obtaining the breaker and finding a spot large enough to accept a double pole outlet?

There's a lot to getting the job done including getting the electrical permit if one is required.

A liitle more info will help. Is it a long run, underground, does it have to go through Attic?
Could be from 15 Amps and up, wire is Expensive, the Load intended will determine the Wire and Breaker. Bigger the wire, more the money.