The Statue of Liberty is the official symbol of the Libertarian Party, but the porcupine is used to represent libertarianism because it is a defensive animal that doesn't harm anyone who leaves it alone. For this reason, many libertarian groups and publications, including the Free State Project, use the porcupine for a mascot.
The libertarian porcupine was originally designed by Kevin Breen in 2005-2006 mimics the Republican Elephant and Democratic Donkey. It has since been used to represent many local libertarian groups, and it has been included on major libertarian publications.

This svg version was uploaded by Lance W. Haverkamp in June 2013, and recolored by MB298 in July 2016 to match the colors used on other parties' mascots.
Libertarian Party Porcupine (USA).svg
Kingofthedead; original by Lance W. Haverkamp