That is not just a simple sound effect, but quite a lot of manipulation. It sounds like they have made heavy use of resonant filters, possibly an auto-tune effect, and reverb.
Here a little sample (attached) of a similar (but different) effect using Audacity 1.3.5
The method used here was:
Recording of baby
Normalize
Select very short part between zero crossing points and repeating them between 20 and 100 times - this draws out some “notes”
Apply the Leveller effect (set to “heavy”) a couple of times to even out the volume.
Amplify by -30dB (the next effect will create a lot of gain).
Apply several “comb filters” by entering similar code to this in the “Nyquist Prompt”
(scale 0.5 (sim (comb s 0.5 275)(comb s 0.5 220)(comb s 0.5 330)(comb s 0.5 375)))
If the resulting sound is too loud and clips, reduce the “0.5” to a smaller value where it says “scale 0.5”
Changing the numbers (275, 220, 330, 375), will result in different sounds.
7) Apply the Leveller effect again.