  We demonstrate that nuclear spin fluctuations lead to the electric current
noise in the mesoscopic samples of organic semiconductors showing the
pronounced magnetoresistance in weak fields. For the bipolaron and
electron-hole mechanisms of organic magnetoresistance, the current noise
spectrum consists of the high frequency peak related to the nuclear spin
precession in the Knight field of the charge carriers and the low frequency
peak related to the nuclear spin relaxation. The shape of the spectrum depends
on the external magnetic and radiofrequency fields, which allows one to prove
the role of nuclei in magnetoresistance experimentally.
