To the Editor:

William Safire's entertaining ''Auguring Well'' (Jan. 21) referred to the option the President has to ''swear'' or ''affirm'' his intention to execute the duties of office. Mr. Safire mistakenly noted, ''Of the 40 men who have taken that oath, only Herbert Hoover chose 'affirm.' ''

Franklin Pierce, our 14th President, chose to ''affirm'' rather than to ''swear.''

He did this as a result of the death of his 11-year-old son, Benjamin, killed in a train accident about two months before Pierce took the oath. Pierce believed the death of his son was a punishment for his sins, so he did not employ the Bible during the inauguration. This action necessitated substituting ''affirm'' for ''swear.''

THOMAS VINCIGUERRA

Garden City, L.I., Jan. 22, 1985