The U.S. Constitution was entirely hand-penned by a calligrapher. So was the Declaration of Independence.
One of the most popular fonts of the time was Caslon which Benjamin Franklin used in his print shop.
A similar font to the lettering in the U.S. Constitution is Declaration Pro by P22 Type Foundry which is derived from the calligraphy in the Declaration. .
Variations include Alternatives, Script, dingbats and Blackletter.
Included in the package is scanned signatures of all the signers of the Declaration of Independence.
The dates on my font files are 2007 and 2015.