Optical and X-ray observations suggested that the 9.38 h binary, SWIFT J0746.3-1608 could be a cataclysmic variable (CV) of the magnetic or nova-like type, or a low-mass X-ray binary. Its optical, UV, and X-ray light curves are strongly variable over years. We report on a recent XMM–Newton observation (2018 April 28), when the source had recovered from a deep low state that likely begun mid-late 2011. We detect for the first time a signal at about 38 min that we interpret as the rotation of the accreting white dwarf primary. Its amplitude decreases with increasing energy, indicating localized photoelectric absorption from cold material. The X-ray spectrum shows optically thin thermal emission with excess at the iron complex, absorbed by a dense medium partially covering the X-ray source. Based on these features, we propose that SWIFT J0746.3-1608 is a magnetic CV of the Intermediate Polar (IP) type. The long-term light curves at different wavelengths show high and low states, a rare phenomenon in the IP subclass and observed so far in only three other systems. The long orbital period, the peculiar long-term variability, and its proposed magnetic nature makes SWIFT J0746.3-1608 an interesting evolutionary test case.