Optical spectroscopic and photometric observations of the hard X-ray-emitting HEAO 1 cataclysmic variable, H0534-581, are presented and interpreted. Two spectroscopic periods are identified at ∼6 and 2.1 hr from measurements of the emission-line radial velocities, which we conclude are the orbital and white dwarf spin periods, respectively. The spin-modulated velocity curves of the narrow and broad emission components are ∼180° out of phase, and the latter has a larger K velocity and more negative γ velocity. Radial velocity curves of the profile wings, determined using a double Gaussian convolution method, indicate that there is a smooth variation in the curve parameters (K velocity, γ velocity, and phase) from the core-dominated regions of the profile into the wings. Magnetospheric disruption of the accretion disk close to the white dwarf (∼10-20R1), followed by forced corotation, spiral streaming, and pseudoradial infall in an accretion funnel, is the mechanism we use to explain the velocity and line profile behavior. The derived mass function of ∼5 × 10-3 M⊙ implies that the orbital inclination is certainly less than 40°, and probably less than 26°, for an empirically derived (from Porb) secondary star mass of ∼0.6 M⊙. An upper limit estimate of the inner disk radius is equated to the magnetospheric radius to derive an estimated surface magnetic field strength of less than 6 MG for M1 < 1 M⊙. A time series analysis of extensive UBVRI and high-speed photometry has resulted only in the identification of the orbital period (6.5 hr) and two puzzling but reasonably persistent periods at 2707 and 1938 s, neither of which can be explained adequately in terms of fundamental periods or sidebands. Reanalysis of EXOSAT time series data has revealed the possible presence of the 2.1 hr spin period, with pulse fractions of 17% and 36%, respectively, for the 2-6 keV (ME) and 0.1-2 keV (LE1) bands. These results indicate that H0534-581 is a new member of the intermediate polar (or DQ Herculis) class of magnetic cataclysmic binaries. This is supported by the observed second radial velocity period, the extreme hardness of the X-ray spectrum (kT > 30 keV), a large Lx/Lopt of ∼5, and the presence of strong He II γ4686 emission. The Balmer decrement indicates a central disk/magnetosphere temperature of ∼105 K.