  Magnetic fields pervade in the interstellar medium (ISM) and are believed to
be important in the process of star formation, yet probing magnetic fields in
star formation regions is challenging. We propose a new method to use Faraday
rotation measurements in small scale star forming regions to find the direction
and magnitude of the component of magnetic field along the line-of-sight. We
test the proposed method in four relatively nearby regions of Orion A, Orion B,
Perseus, and California. We use rotation measure data from the literature. We
adopt a simple approach based on relative measurements to estimate the rotation
measure due to the molecular clouds over the Galactic contribution. We then use
a chemical evolution code along with extinction maps of each cloud to find the
electron column density of the molecular cloud at the position of each rotation
measure data point. Combining the rotation measures produced by the molecular
clouds and the electron column density, we calculate the line-of-sight magnetic
field strength and direction. In California and Orion A, we find clear evidence
that the magnetic fields at one side of these filamentary structures are
pointing towards us and are pointing away from us at the other side. Even
though the magnetic fields in Perseus might seem to suggest the same behavior,
not enough data points are available to draw such conclusions. In Orion B, as
well, there are not enough data points available to detect such behavior. This
behavior is consistent with a helical magnetic field morphology. In the
vicinity of available Zeeman measurements in OMC-1, OMC-B, and the dark cloud
Barnard 1, we find magnetic field values of $-23\pm38~\mu$G, $-129\pm28~\mu$G,
and $32\pm101~\mu$G, respectively, which are in agreement with the Zeeman
Measurements.
