The Ibrox club were on Monday drawn to play United in the fifth round in February, with supporters' groups immediately calling for a stay-away protest for the first match away to Scottish Premier League opposition since they were relaunched as a new company and denied entry to the SPL.
Some Rangers fans believe United chairman Stephen Thompson was an influential figure in their demotion to the Third Division.
Thompson had also refused to refund Rangers fans when a match at Tannadice between the two clubs in 2009 was abandoned at half-time due to adverse weather conditions.
In his statement confirming that the Ibrox club would not be taking any tickets, chief executive Charles Green said: "Everyone at this club is dismayed at the actions of certain SPL clubs, which were actively engaged in trying to harm Rangers when we were in a perilous situation and we are acutely aware of their attitude to us."
It is understood United have a board meeting on Wednesday with the issue on the agenda, but a lengthy joint statement from ArabTRUST and The Federation of Dundee United Supporters Clubs, read: "It's with great disappointment that we read Rangers' official statement indicating that they will not take up their ticket allocation for the Scottish Cup tie in February.
"In a time when Scottish football needs to look to the future and how we can rebuild our game, it's sad that some parties choose to refer to past alleged indiscretions against their club as an excuse to not attend the match.
"In the instances referred to by Rangers supporters, a court of law decided that Dundee United had acted appropriately in respect of ticketing post the abandoned game in 2009.
"As for the decision by the SPL to take action against Rangers in the summer, this was made by the majority of clubs - not only Dundee United."
Rangers' announcement brings into question whether they will be entitled to share in the revenue generated by the fixture.
A Scottish Football Association spokesperson said: "The matter will be discussed at the SFA board meeting on Thursday."
The issue was also addressed in the United fans' statement.
"We believe that the stance taken by Rangers brings them into disrepute in respect of the Scottish Cup," it read.
"We therefore call on the SFA to act strongly, in particular by stating that the normal competition rules in respect of an equal split of gate money do not apply in this case and that all revenues should be retained by Dundee United.
"We also put trust in the SFA using their powers to ensure that fans are free to choose whether to attend games or not and that our competitions, which rely on spectator participation to ensure continued commercial and media profile, are not devalued as a result of the actions of one member club against another."
The statement continued: "We call on all Arabs to pack Tannadice and get behind the team in February.
"The tie is a fantastic opportunity for our club to progress to the quarter final of the Scottish Cup and be just one game away from Hampden.
"As supporters bodies, we do not agree with any boycott - fans are the lifeblood of the game.
"We believe that all clubs and fans need to work together for the good of the Scottish game, rather than continue debating decisions made in the past which many have long moved on from."