We present optical and X-ray time-series photometry of EI UMa that reveal modulation at 746 and 770 s, which we interpret as the white dwarf spin and spin-orbit sidebands. These detections, combined with previous X-ray studies, establish EI UMa as an intermediate polar. We estimate the mass accretion rate to be ~ 3.6 x 10^{17} g s^{-1}, which is close to, and likely greater than, the critical rate above which dwarf nova instabilities are suppressed. We also estimate the white dwarf to have a large magnetic moment mu > (3.4 +/- 0.2) x 10^{33} G cm^3. The high mass accretion rate and magnetic moment imply the existence of an accretion ring rather than a disk, and along with the relatively long orbital period, these suggest that EI UMa is a rare example of a pre-polar cataclysmic variable.
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