Scottish fans are to be given the choice between "Flower of Scotland" and an alternative national anthem - written by Germans.
Scotland players presently sing "Flower of Scotland"
"Highland Cathedral" has already been played at international matches.
SRU marketing chief Phil Anderton said: "Our plan is to introduce it at one of the games alongside 'Flower of Scotland', then to gauge the feedback."
The pipe tune was written by German musicians Ulrich Roever and Michael Korb in 1982.
It has now been given words by poet Donald Smith.
"Flower of Scotland" has in the past decade been adopted by Scotland's football and rugby associations as the nation's unofficial national anthem.
But some criticise the song written by the late Roy Williamson, of folk group The Corries, for being anti-English.
Smith said: "There's a need to bring in something new for this new Scotland we are trying to create."
However, Smith also faces a rivalry, with tenor Ben Kelly having penned his own lyrics for "Highland Cathedral".
"Flower of Scotland" and "Highland Cathedral" are likely to be played side-by-side at the Six Nations match against France at Murrayfield in March.