  The parsec-scale Faraday rotation measure (RM) distribution of six "blazars"
is investigated using multi-frequency (4.6--43 GHz) polarization observations
taken on 2006 July 2 with the VLBA. Analysis of the RM provides the direction
of the line-of-sight (LoS) magnetic field component, as well as the intrinsic
2-D polarization distribution on the plane of the sky. Our results show that
the magnitude of the core RM increases systematically with frequency, and is
well described by a power-law, where |RM_{core}| \propto \nu^a. Our measured
values of $a$ vary from 0.9 to 3.8, providing information on the assumed
power-law fall-off in the electron density with distance from the central
engine for each source. RM gradients were detected across the jets of three
sources, supporting the presence of helical magnetic fields in a sheath or
boundary layer surrounding their jets. We find a bi-modal distribution of the
intrinsic jet polarization orientation; either aligned or orthogonal to the jet
direction. A helical magnetic field geometry can neatly explain both the
bi-model distribution of the jet polarization orientation and the ordered
polarization structure detected on these scales. In half the sources, we find
that the core RM changes sign with distance from the central engine. We provide
an explanation for this by considering a boundary layer of Faraday rotating
material threaded by a helical magnetic field, where bends in the relativistic
jet or accelerating/decelerating flows give rise to changes in the dominant LoS
components of the magnetic field, which in turn gives rise to different signs
of the RM. (abridged)
