What gauge wire will transfer 220 volts 250' and serve 15 amps?

A 300 MCM copper conductor will limit the voltage drop to 3% or less when supplying 125 amps for 500 feet on a 250 volt system.

On a situation like this two Transformers might be considered. One to boost the voltage to a higher level. This allows a smaller and less expensive conductor to be used between the two transformers and then drop the voltage down at the load end to feed the load at the recommended value.

Price out the cost of the 300MCM conductor and then compare that against the cost of the two transformers and the new smaller wire size. By boosting the voltage to 600 volts between the transformers the wire can be reduced to a 1/0 copper conductor. This will limit the voltage drop to 3% or less when supplying 125 amps for 500 feet on a 600 volt system.