Yes — fresh ginger is safe in small amounts and is even thought to help with nausea and digestion in birds.
Keeper's noteA thin sliver of fresh ginger, grated into chop, is the usual way. Skip candied ginger (sugar) and concentrated ginger oils.
Why ginger is good for parrots
Fresh ginger root is non-toxic and contains anti-inflammatory compounds; many keepers offer a little to birds prone to motion sickness (e.g., before car travel) or digestive upset. It's strong-flavored, so birds take only small amounts, which is exactly right.
How to serve it
A small amount of fresh root, grated or thinly sliced.