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.
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