A spokesperson for English rugby's governing body said the organisation needs to do more to "grow awareness".
The Black Lives Matter movement has been embraced in several sports, with Premier League players taking a knee on Wednesday.
"We need to do more to achieve diversity," an RFU spokesperson said.
"And we are determined to accelerate change and grow awareness.
"The Swing Low, Sweet Chariot song has long been part of the culture of rugby and is sung by many who have no awareness of its origins or its sensitivities.
"We are reviewing its historical context and our role in educating fans to make informed decisions."
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The first known use of the song at Twickenham was in 1987, when Martin 'Chariots' Offiah played in the Middlesex Sevens tournament.
It is thought Swing Low, Sweet Chariot was written in the mid-19th century by Wallace Willis, who was a black slave.
England's Maro Itoje, who spoke about rugby and race on the Rugby Union Weekly podcast, recently said the song had a "complicated" background.
Last week World Cup winner Maggie Alphonsi - the only black person on the RFU council - said that the death of George Floyd in the United States had led to "powerful conversations".
RFU chief executive Bill Sweeney has vowed to increase diversity in the organisation, saying:
"We have undertaken some very good initiatives at the grassroots level to encourage more diverse participation however, that in itself is not enough.
"We need to do more to achieve diversity across all areas of the game including administration."