We present time-resolved spectroscopy and circular spectropolarimetry of the SW Sex star RX J1643.7+3402. We find significant polarisation levels exhibiting a variability at a period of 19.38 +- 0.39 min. In addition, emission-line flaring is found predominantly at twice the polarimetric period. These two findings are strong evidences in favour of the presence of a magnetic white dwarf in the system. We interpret the measured periodicities in the context of our magnetic accretion model for SW Sex stars. In contrast with LS Pegasi -the first SW Sex star discovered to have modulated circular polarisation- the polarisation in RX J1643.7+3402 is suggested to vary at 2(omega - Omega), while the emission lines flare at (omega - Omega). However, a 2omega/omega interpretation cannot be ruled out. Together with LS Peg and V795 Her, RX J1643.7+3402 is the third SW Sex star known to exhibit modulated circular polarisation.
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