Easdale, who was appointed to the football board on Saturday but is not a member of the PLC board which is at the centre of a power struggle, now has a shareholding of 4.37 percent, according to a statement made to the London Stock Exchange.
The statement read: "The company announces that it was notified today, 17 September 2013, that on 10 September Alexander (Sandy) Easdale, acquired 2,125,000 ordinary shares of 1 pence each in the company.
"Following the acquisition, Mr Easdale holds 2,842,957 ordinary shares, representing 4.37% of the issued share capital of the company."
Last month the Greenock-based businessman claimed to hold the largest shareholding at Rangers after securing a "binding agreement" to buy the shares of former chief executive Charles Green. Easdale's brother, James, is on the PLC board.
In a statement on August 30, Sandy Easdale - who runs his various business interests alongside brother James, including McGill's Buses - said: ''There has been continued speculation and constant enquiries to buy this largest holding in Rangers but Mr Green gave me the first option which I exercised. Between my family holdings and through other supporting investors I now have the largest shareholding in Rangers Football Club.''
Earlier in August, Rangers announced to the Stock Exchange that Isle of Man-based investment firm Laxey Partners had increased its shareholding to 6.53 percent.