Board Thread:The Reference Desk/@comment-172.7.49.112-20160802214828/@comment-1350697-20160804163753

Though Missy seems to be aware enough of one to celebrate it, there's no specific date that I'm aware of that's ever come up as "this is the day on Earth's Gregorian calendar that the Doctor would celebrate his birthday on."

Of course, because time travel, the Doctor is almost certainly out-of-sync from whatever the date, be it Gregorian or Gallifreyan, of his birth would be.