  We study the polarization properties of 22 known rotating radio transients
(RRATs) with the 64-m Parkes radio telescope and present the Faraday rotation
measures (RMs) for the 17 with linearly polarized flux exceeding the off-pulse
noise by 3$\sigma$. Each RM was estimated using a brute-force search over trial
RMs that spanned the maximum measurable range $\pm1.18 \times 10^5 \,
\mathrm{rad \, m^2}$ (in steps of 1 $\mathrm{rad \, m^2}$), followed by an
iterative refinement algorithm. The measured RRAT RMs are in the range |RM|
$\sim 1$ to $\sim 950$ rad m$^{-2}$ with an average linear polarization
fraction of $\sim 40$ per cent. Individual single pulses are observed to be up
to 100 per cent linearly polarized. The RMs of the RRATs and the corresponding
inferred average magnetic fields (parallel to the line-of-sight and weighted by
the free electron density) are observed to be consistent with the Galactic
plane pulsar population. Faraday rotation analyses are typically performed on
accumulated pulsar data, for which hundreds to thousands of pulses have been
integrated, rather than on individual pulses. Therefore, we verified the
iterative refinement algorithm by performing Monte Carlo simulations of
artificial single pulses over a wide range of S/N and RM. At and above a S/N of
17 in linearly polarized flux, the iterative refinement recovers the simulated
RM value 100 per cent of the time with a typical mean uncertainty of $\sim5$
rad m$^{-2}$. The method described and validated here has also been
successfully used to determine reliable RMs of several fast radio bursts (FRBs)
discovered at Parkes.
