The Whydah Pirate Museum in Yarmouth, Massachusetts, publicly displayed the bone Monday. The bone was found near what is believed to be Bellamy's pistol.
The objects were pulled from the Whydah Gally shipwreck several years ago.
The museum has enlisted forensic scientists to extract DNA and compare it with DNA from a living Bellamy descendant. Testing will take about a month once it gets the sample.
The Whydah sank in 1717. The wreck was discovered in 1984. Most of its treasure is thought to remain on the ocean floor.
The museum calls it America's version of King Tut's tomb.