We study the growth and structure of thin films of the organic semiconductor rubrene during organic molecular beam deposition (OMBD) on silicon oxide in situ and in real time using X-ray scattering. Using in situ grazing incidence diffraction (GID) we find a small degree of local order but an otherwise largely disordered structure, consistent with out of plane scans. Monitoring the surface morphology in real time during growth, we find relatively smooth films (surface roughness sigma below approximately 15 A for thicknesses up to at least 600 A) and a significant delay before the onset of roughening. This anomalous roughening in the beginning and crossover to normal roughening later during growth may be related to conformational changes of rubrene in the early stages of growth.