Speaking on Fox News, the real estate mogul turned candidate described the situation as "an unbelievable humanitarian problem".
Thousands of people, mainly from Syria, have been entering Europe and travelling northwards in recent weeks.
The US has allowed 1,500 Syrians to re-settle since the start of the conflict.
But there are hints that it will take more.
Speaking from the US Capitol on Wednesday, US Secretary of State John Kerry said the US was committed to welcoming more Syrian refugees.
The UN High Commissioner for Refugees (UNHCR) has asked governments around the world to resettle 130,000 Syrians by the end of 2016. In past conflicts, the US has typically taken half of the UNHCR request.
"On a humanitarian basis, something does have to be done," Mr Trump said.
"It's a serious problem. We haven't seen anything like it since the second world war, and it's getting worse and worse".
When asked whether he thought they should be allowed in the US, the business mogul said: "I hate the concept of it, but on a humanitarian basis, with what's happening, you have to."
He added: "It's living in hell in Syria. They are living in hell."
Mr Trump has made a tough line on immigration a central plank of his campaign, and has drawn criticism for anti-immigrant views in the past.
He was harshly criticised after saying undocumented Mexican immigrants were "bringing drugs, they're bringing crime, they're rapists".
The migrant crisis has had European leaders scrambling to come up with a solution.
On Wednesday, European Commission President Jean-Claude Juncker announced a plan for 120,000 additional asylum seekers to be distributed among EU nations, with binding quotas.
Mr Trump's views on the migrant crisis mark him apart from some of his Republican rivals who have been more hardline in their views.
They will all be appearing on stage next week in a televised debate hosted by CNN, and the millionaire businessman has asked the CNN president to donate the advertising revenue to charities for army veterans.
The "tremendous increase in viewer interest and advertising is due 100% to Donald J Trump," he wrote.
Leading Republican presidential candidate Donald Trump has said the US should take greater steps to address the migrant crisis in Europe.