The march began at about 14:15 BST in St Helen's Square before making its way to York Minster.
The crowd was then addressed by representatives of charities and pressure groups as well as refugees.
March organiser Harkirit Boparai, from York Human Rights Network, said: "What we've seen through this demonstration is the community spirit of York".
David Cameron announced on Monday that the UK would accept up to 20,000 people from camps surrounding Syria with priority given to vulnerable children.
A spokesperson for City of York Council said: "The council is meeting partners from across the city to identify how York can best provide support, as we await information from the government on how the process of resettlement will work."
Hundreds of people have taken part in a "York says refugees welcome here" rally in the city centre.