The call comes ahead of a crucial vote in the House of Commons on Tuesday, with a majority of MPs expected to vote against the deal proposed by Prime Minister Theresa May.
Mr Rennie addressed parliamentarians, councillors, campaigners and activists at a gathering in Milngavie on Saturday.
Mr Rennie said: “It speaks to the heart of our values as liberals to stand with our neighbours in the UK and Europe because through partnership we can achieve so much more.
“Two years ago, Liberal Democrats stood alone in saying the public should have the chance to think again if Brexit turned out not to deliver what was promised.
“Now we are part of a movement. The Scottish Parliament has voted for a People’s Vote, trade unions and business groups have backed it and poll after poll has shown support growing across the whole UK.”
The UK is expected to depart the European Union on March 29, although there have been calls to extend the deadline.
The Government was defeated last week in a vote at Westminster which means that they will have to come up with revised plans within three days if Mrs May’s EU withdrawal deal is rejected by MPs.
Mr Rennie said: “With concern palpable among the extremist wing of the Conservative party that Brexit can be stopped, it is clear Liberal Democrats are closer than ever to securing a People’s Vote.
“It is time MPs, particularly the Labour leadership, explored their conscience and supported that growing campaign. We need one more push to deliver a People’s Vote and a chance to remain in the EU.”