However, RIFC's new board has been unable to appoint a new advisor before Thursday's deadline to remain listed expired.
The suspension of shares came after the removal of the previous board by a shareholder group led by former director Dave King. RIFC said that it is in negotiations to move trading to a different platform.
According to BBC Scotland although shares can still be traded privately, a number of Rangers shareholders are considering legal action following news of the club's delisting from AIM.
That includes the group for whom former football board chairman Sandy Easdale held proxies for around 20% of Rangers shares.
It is also understood that at least one complaint has been made to the Financial Conduct Authority, but that body has no jurisdiction over Rangers.
But Rangers say the fault lies with the previous regime, which included Easdale, and said: "It is simply the result of the well-documented failings in corporate governance and management of those who previously controlled the company."
The club said AIM received "more complaints about the company than any other company on its exchange over the last year".
At the time of the extraordinary meeting that deposed the previous board, South Africa-based King expressed his confidence that a new nomad could be appointed.
King, who has convictions for contravening South African tax laws, had hoped to be appointed to the board.
Rangers said the prospective nomad completed its checks on the "fit and proper" status of the existing directors and the proposed additional director.
However, after the nomad's assessment of the "company's profile" in recent years and discussions with the Stock Exchange, it was unable to "take up appointment", Rangers said.
"We also understand that any alternative nomad is liable to encounter similar difficulties and therefore the company requires to terminate its listing on AIM," they stressed.
Chairman Paul Murray added: "However, I must point out that delisting will have no effect on our overall financial strategy.
"The investments we expect will still be made and Rangers will be rebuilt on schedule."
One avenue being explored is RIFC being listed on the ISDX, the successor to the Plus platform, where The Rangers Football Club plc's shares were traded in the past and where the shares of Arsenal are listed.
Until then, shareholders will from Tuesday have access to "a matched bargain-trading facility" with JP Jenkins, a founding member of the AIM and Ofex markets through which Millwall's shares are already traded.
Rangers Supporters' Trust said: "It is unfortunate that the company is having to delist because of the mismanagement and, at times, malicious neglect of previous directors and nomads of the company."