You don't. However, you can lure him back to his owner using the cracker, which is inside Petey's Pub on the upper left side.
The parrot will send you to jump into the sea, then appear at an upper window of the Trading Post. After you block the vent (chimney) at the Pub, he is in the palm tree at the far right. When you go to see his owner at the tower by the docks, you can use the cracker right there to bring the parrot over to you. Click the pirate to get the map piece.
parrot port.
If you look at the island in the middle it is to the right of it
Parrot Port
Usually Parrot Port, for between 32 and 40 doubloons.
It is the island directly to the right of Fort Ridley, in the 3 o'clock position on the island map.
You find the navigator in the second floor of the bar at parrot port.
It's on top of the pub (on the chimney).
Parrot Port has the highest price on medicine. It is the island in the easternmost island.
Parrot Port- it is the island to the immediate right of Fort Ridley
At Parrot Port, the "vent" is the chimney on the roof of Petey's Pirate Pub.
YOURSELF! Stand on it long enough to satisfy the parrot
On top of the barrels inbetween the first house and the trading post.