The Wild Turkey is the True American Bird but none have appeared on
United States coins until 2013.
Before then there were only tokens and medals, here is one:

Token - New Orleans Mardi Gras Wild Turkey 1978 (38mm)
FISH and GAME of NORTH AMERICA / WILD TURKEY / 1978
JEFFERSON CITY BUZZARDS / MARDI GRAS / SINCE 1890 / N.O.L.A.
Then in 2013, a bird whose time has come:

United States
Sacagawea dollar 2013 - Treaty with the Delawares 1778
Delaware Indian tribal animals Wild Turkey, Wolf, Turtle
And in 2015, I got my wish, a wild turkey on an official circulating United States coin:

United States quarter (25 cents) 2015 - America the Beautiful - Kisatchie National Forest, Louisiana
Kisatchie, we have liftoff (and yes, they can fly)
And, outside of the United States, another wild turkey on a coin:
The small country of Andorra issued this coin in 2002:

Andorra brass 5 cèntims 2002
Gall Fer or Capercaillie
The Krause
2002 Standard Catalog of World Coins (29th Edition) had this description of the coin:

Andorra brass 5 cèntims 2002 - Krause Catalog description as "male turkey"
Turkeys are native to Mexico and do not exist in the wild in Europe. A Capercaillie is a big European bird sometimes weighing 7 kg or 14 lbs.
The 2005 edition of the Krause Catalog still had the "male turkey" description.
Finland also issued a coin with the Capercaille bird on it:

Finland 10 Markka 1994 Capercaillie
Bi-metallic copper-nickel brass
The Finland coin bird is correctly described in the Krause Catalogs.
And another turkey relative on a coin:

Korea Half Chon 2002 Guinea Fowl
Guinea Fowl are originally from Africa but are now domesticated birds.
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