Anything that contains carbon 14 can be dated using radiocarbon dating. This means anything that is organic (was once alive) can be dated using radiocarbon dating. It is unlikely to use radiocarbon dating for a brain, however, because a brain will usually decompose. Dating a brain found in a frozen human however would be theoretically possible.
Like the other person answered, it would be hard to date a brain as it usually decomposes without leaving a fossil. Also, it depends on the age of the item being dated. Carbon dating is only precise enough for things younger than about 60,000 years, and has a fairly large uncertainty (about +/- 40 years for anything under 10,000 years old). On top of that uncertainty there is a calibration based uncertainty (due to the need to compare the raw measurements with measurements of atmospheric carbon-14). This adds +/- 16 years for dates under 6,000 years, and +/- 163 years for dates approaching 26,000 years ago. What all those numbers mean is that if you need high precision dating involving recent human history, carbon dating might not be the answer.
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