The estimated Â£4.3bn cost of the initiative would be paid back over time by the taxes paid by those who settle in Britain, he said.
The government said it would accept 20,000 Syrian refugees by 2020 - but Labour said the figure was inadequate and urged ministers to do more.
Mr Farron claimed the UK had "taken a pitiful number of people".
The Lib Dem leader said ministers had only accepted refugees "under extreme pressure".
"For all that we focus on Brexit, and lots of other things as well, the biggest humanitarian crisis facing our continent is still going on and Britain is turning its back and pretending it's not happening," he said.
"If you show confidence in people and give them sanctuary they become very loyal citizens.
"We are only talking about 50,000 people. We are talking about doing what is right."
The move, along with reopening the programme to settle lone child refugees, will be fully costed in the Lib Dem manifesto, Mr Farron said.
The Lib Dem leader, visiting a refugee charity in Gloucestershire on Thursday, said the numbers of new arrivals would be absorbed over five years.
In 2015, former Conservative prime minister David Cameron said the UK had a "moral responsibility" to take in 20,000 refugees living in camps bordering Syria.
Britain should provide sanctuary to 50,000 Syrian refugees, Liberal Democrat leader Tim Farron has said.