We report photometry and spectroscopy of the novalike variable DW Cancri. The spectra show the usual broad H and He emission lines, with an excitation and continuum slope characteristic of a moderately high accretion rate. A radial-velocity search yields strong detections at two periods, 86.1015(3) min and 38.58377(6) min. We interpret these as respectively the orbital period P_orb of the binary, and the spin period P_spin of a magnetic white dwarf. The light curve also shows the spin period, plus an additional strong signal at 69.9133(10) min, which coincides with the difference frequency 1/P_spin-1/P_orb. These periods are stable over the 1 year baseline of measurement. This triply-periodic structure mimics the behavior of several well-credentialed members of the DQ Herculis (intermediate polar) class of cataclysmic variables. DQ Her membership is also suggested by the mysteriously strong sideband signal (at nu_spin-nu_orb), attesting to a strong pulsed flux at X-ray/EUV/UV wavelengths. DW Cnc is a new member of this class, and would be an excellent target for extended observation at these wavelengths.