Buy Rangers, the fan' ownership scheme run by the Trust, has bought another 200,000 shares in the Ibrox club.
The scheme purchased 357,000 shares for a total of £250,000 at the IPO back in December 2012.
This latest outlay takes their stake in the club from 0.55% to 0.85%.
And having increased its shareholding to 557,856, Dinnie is hopeful they can double that in the future.
He said: "It's a tremendous achievement for our members to reach this level of ownership through our BuyRangers community share scheme.
"The next target for us is to own a million shares in the club."
It is just two months since direct debits into the scheme started and Trust officials are encouraged by the take-up.
Rangers supporters who would like to have a greater say in the running of their club are being asked to invest £12.84 a month.
RST board member Gordon Stewart said: "A small number of shares became available on the open market and BuyRangers have bought them.
"But the direct debits in BuyRangers only started in December. We have used the money we had left over after the IPO and the money we had taken in direct debits for this purchase.
"We now have an 0.85% stake in the club. It may not sound much but we aim to build on this regularly as the months move on.
"A few hundred of Rangers supporters have signed up to the scheme already. But it is an ongoing process.
"If we can get a couple of hundred fans signing up to the BuyRangers scheme every month we will be able to steadily increase our stake in the club over time."
Dinnie added: "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 Trust was the 26th largest shareholder in Rangers after the IPO. This now takes us another step in the right direction.
"This latest purchase of shares demonstrates that fans have the ability to organise themselves properly and on a scale that can make a difference to the club."