I've looked for an hour and it seems really hard to find. From what I've seen, (a) birds have a different brain structure than mammals (“general intelligence” originates in other parts of the brain), and (b) their neuron count changes hugely (relative to mammals) during their lifetimes. I've seen lots of articles giving numbers for various species and various brain components, but nothing in aggregate. If you really want a good estimate you'll have to read up to learn the brain structure of birds, and use that together with neuron counts for different parts to gather a total estimate. Google Scholar might help in that endeavor.