We report intermediate resolution spectroscopy (50 km/s) of the magnetic Cataclysmic Variable AE Aqr performed as part of the World Astronomy Days (WAD) campaign. Our analysis of the absorption features supports a K4 classification for the companion star, which contributes more than 95% of the total flux in the range 600-700 nm. We find that the companion star fills its Roche lobe since we detect a 10% modulation in the rotational broadening (V sin i) of the absorption fines, due to the changing geometry. Model fitting to the V sin i(phi) curve enables us to measure directly the system inclination (i = 58 +/- 6 deg) and the gravity darkening coefficient (beta = 0.08 +/- 0.01). Improved orbital parameters are also presented, including an updated mass ratio (q = K1/K2 = 0.630 +/- 0.012) based upon our K2 value and the spin-pulse delay. An independent determination of q is also provided by correcting the phase-averaged V sin i for non-spherical effects. The need for these two values to agree constrain the limb-darkening coefficient to be epsilon approximately equal to 0.40 (for beta = 0.08). The component masses derived from our values of K2, q and i are M1 = 0.79 +/- 0.16 solar mass units and M2 = 0.50 +/- 0.10 solar mass units. In addition, we do not see spectral evidence of irradiation effects.