Yes — fresh apricot flesh is a great source of vitamin A, but remove the pit, and go easy on dried apricots.
Keeper's noteFresh, pitted apricot is excellent. If buying dried, choose unsulphured (they're brown, not bright orange) and offer only small amounts.
What to watch out for with apricots
Apricots are rich in beta-carotene (vitamin A), which pet parrots often lack. The flesh is safe; the pit's kernel contains amygdalin (cyanide-releasing), so it must go. Dried apricots concentrate the sugar and often carry sulfite preservatives, so fresh is far better.