Mr Farron said the country should let in around 60,000 people as part of a joint European response to the refugee crisis.
Farron is up against former Health Minister Norman Lamb for the leadership position, following the resignation of Nick Clegg after May's general election.
Speaking to The Observer, he said his party should support an EU quota system, under which refugees would be shared out between member states.
He said: "We should support this because we are decent people.
"Our party should not have mixed messages about this.
"We should not turn people away."
In the past he has written to David Cameron discussing how the UK should be proud to help refugees, using the example of Ugandan Asians who were expelled under Idi Amin in 1972.
"First and foremost it is about compassion, but also there is enlightened self-interest."
These are the first comments by a senior UK politician in favour of a quota system put forward by the EU, which is backed by Germany and Italy.
Mr Farron was speaking after further disruptions at Calais in France, following reports around 150 migrants tried to storm the Channel Tunnel
David Cameron did not back the EU's plans on a quota system, instead saying the reason people leave should be addressed instead:
He said: "Why so many people want to leave their home countries and by taking measures to thwart the network of people who traffic them across the Mediterranean."
The result of the Liberal Democrat leadership election will be announced 16th July.
