Is there anyone who got their psychic power through science?
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.