The Campaign for Borders Rail aims to raise £10,000 to help create a "fighting fund" to achieve its ambitions.
It comes after UK and Scottish Government ministers joined the leaders of five councils in the Borders in July to sign heads of terms for a £394.5 million cross-border economic deal.
The formal agreement is a major step towards signing a full deal to fund proposals including a feasibility study into extending the Borders Railway line from Tweedbank to Carlisle.
The UK Government is investing up to £265 million, £200 million of which is going south of the border, while the Scottish Government has pledged £85 million and the five local authorities will contribute a total of £44.5 million.
The growth deal is the first cross-border deal of its kind, bringing together five cross-border local authorities - Dumfries and Galloway Council, Scottish Borders Council, Carlisle City Council, Cumbria County Council and Northumberland County Council.
Simon Walton, chairman of the CBR campaign, said: "The generosity and commitment of the membership continues to impress me.
"They've consistently contributed to the running of the campaign but the financial burden of engaging with governments and agencies up and down the country cannot be borne solely by those dedicated individuals.
"We have 10 times that number who informally support the campaign so we've launched a wider fundraising initiative to let that wider body offer support, even if they don't feel they can commit to full membership."
CBR said money raised would underwrite the campaign's engagement with stakeholders as the project moves through the critical feasibility study phase.
Mr Walton said: "We are entirely voluntary and we're lobbying for the biggest development project in Britain without any paid officers.
"That's not a boast, it's a tribute to the commitment of the individuals involved with the Campaign for Borders Rail."
The 30-mile Borders Railway route between Edinburgh and Tweedbank was the longest new line built in the UK for more than a century when it was opened by the Queen in September 2015.