The fan group's long-term ambition is to hand control of the club to the Light Blues faithful, and they now hold 557,856 shares after using £52,000 donated by fans using the BuyRangers direct debit scheme to snap up their latest tranche.
However, their stake only equates to 0.86 per cent of the League One leaders' total shareholding, and Trust chairman Gordon Dinnie admits outright power is a long way off.
He said: "There is still a long way to go.
"We started our direct debit scheme just before Christmas. If we can get enough interest going in that then we can buy shares on a monthly basis and build up our stake. We can also borrow against that money coming in and use it to buy more.
"However, the big issue is availability of the shares. With the current price being so low, when you try to buy them on the market, folk are asking for a few pence more. So it's not a case of buying a £1million's worth of shares if there is £1million's worth of shares available.
"But then again, we don't need to aim for anything like a 50 per cent stake in the club. Because of the fractious nature of the shareholding, a 10 per cent stake could give you a major say in how the club is run.
"James Easdale had just one more share in the club than the RST following the IPO (initial public offering), yet he was appointed to the board.
"If we get to five per cent, we would hold the right to call an AGM, and the things you are able to do increases as your stake goes up from that point.
"We need to take it slow but if we can generate enough interest then hopefully we can then look towards taking our holding past one per cent, then five, then as our stake in the club grows we can think about getting a director onto the board of the club that has been elected by the fans."
The RST ploughed £250,000 - including £5,000 pledged by former Ibrox striker Kris Boyd - into Rangers when it was floated on the stock market in December 2012. However, that was not enough to stop controversial former chief executive Charles Green gaining control.
The shares were priced 70p each at that point, but the off-field turmoil surrounding the club since has seen that price tumble to just 25.75p per share.
The RST was able to buy its latest tranche at 26p per share after negotiating the seller down from 29p.
In an email to RST members, Dinnie claims that low value could help the Trust double its stake.
He said: "It's a tremendous achievement for our members to reach this level of ownership through our BuyRangers scheme. The next target for us is to own a million shares in the club.
"The addition of a direct debit option to BuyRangers will be a great help and enable us to buy more shares as and when they become available at a reasonable price."
The RST announcement comes just two days before Supporters Direct Scotland stages a presentation to Rangers fans at the Louden Tavern, Ibrox, about the possibility of setting up a rival scheme.
SDS has already helped Hearts and Dunfermline set up rescue bids for their administration-hit clubs and will now advise the Light Blues' support how they can gain control.
Dinnie refused to criticise the government-backed group for competing with the RST scheme, but insisted the Trust would now step up BuyRangers.
He said: "They say their meeting is a consultation process and not a new scheme, so there is no need for us to stop doing what we're doing. In fact, we're now cracking on with BuyRangers.
"But the long-term aim is to see fan-ownership realised at Ibrox - that has been our reason d'etre for the last 10 years. Their new scheme that could have have worked alongside BuyRangers.
"However, I won't condemn it. It would be ludicrous for me to condemn it when they are working towards the same thing as we are. However, we will carry on with BuyRangers because we think it is the best way forward."