Like a lot of songs attributed to the Revolutionary War period in many books and websites, etc. this was composed long after. The first appearance I have found is in a literary magazine, The Chautauquan, Vol. 9 #3, Dec. 1888, p. 152. The poem is attributed to an Arthur Hale. Edward Everett Hale (a relative of Arthur?) published it with the correct attribution in one one of his books, The Story of Massachusetts in 1891 (p. 298) and again in 1904 in his New England History in Ballads without the attribution where he says the incident described in the song has been verified. This is most likely the source for folks erroneously thinking 'The Yankee Privateer' is from the 1770s.