Is there anyone who got their psychic power through science? On the first episode of To Aru Majutsu No Index, Touma said


  Magic is impossible, psychic powers aren't even rare at this city school. Anyone can invent it with the powers of science.


And Touma himself said that he got his power since he was born.

So, is there anyone in Index and Railgun who become an esper using science?

Note: I haven't finished watching Index, but I've watch Railgun, and I don't think there's anyone able to do this.
Most psychic powers are created by science. Normally, an Esper doesn't have a special ability and only gains it by experiments, special drugs etc. See Power Curriculum Program for more information.

There are some (at the moment 4 known of which only 3 occur in the original works) people who have esper-abilities without being part of the Power Curriculum Program, called Gemstones. The only one that occurred in the anime yet is Himegami Aisa (appeared in Index Episode 7 (Deep Blood Arc)).

Touma himself has no psychic power, his power is of unknown source.

Thanks to Krazer for mentioning the Gemstones in the comments.