We use interstellar scattering of the Vela pulsar to determine the size of its emission region. We find that radio-wave scattering in the Vela supernova remnant broadens the source by 3.3 +/- 0.2 mas x 2.0 +/- 0.1 mas, with the major axis at a position angle of 92 degrees +/- 10 degrees. From the modulation of the pulsar's scintillation, we infer a size of 500 km for the pulsar's emission region, with an estimated uncertainty of about a factor of 2, including systematic errors, We suggest that radio-wave refraction within the pulsar's magnetosphere may plausibly explain this size.