XCOM: Enemy Unknown Cheats
Now that I think about it, it does unlock pretty late, I didn't even get the chance to fully level a psi soldier manually before the end game.
How to get psi abilities:
After a while you'll get the chance to build a facility (forgot the specific name) where you can 'test' your soldiers for psi-aptitude, which takes a few days.
The determination if a soldier is Psychic is done at the moment you begin testing them and seems to be randomly determined. I tried saving on the final day of testing and the outcome was identical for the three soldier each time over 10 reloads. I had one sniper I wanted to by psychic.. so I just tested him. Waited 10 days and reloaded if he failed the test and on the third reload he came up positive.
[Edited by grffnhwk, 10/26/2012 5:26:40 PM]