No, not really.
Electivire can only learn it as an Egg Move.
If you are willing to breed another Elekid again, breed the following:
A male Pokemon that knows Ice Punch, and is part of the Human-Like Egg Group. (A good Pokemon to use would be Hitmonchan)
A female Electivire or Electabuzz (if your Electivire is female, you could use that). Remember, it has to be female so it may cost you finding another one.
Breed the Pokemon together, and the offspring should be an Elekid with Ice Punch.
Hope I helped. :)
Source and other parts of Serebii.