The "Worrying Signs" group invites people to share experiences and concerns and to post pictures and screen grabs relating to any alleged incidents.
Sarah Childs, who voted for Britain to remain in the EU, and is one of the group's creators, told ITV News it was set up in response to a number of incidents that had recently come to their attention.
"We wanted to collect them all together to show people the scale of the problem. It's easy to dismiss one post but when you see the album it's a lot harder.
"We have a lot of people asking us to just move on from the referendum result but the people affected by these incidents can't move on while this is happening," she added.
Ms Childs also said it is hoped that by highlighting this issue "people will realise that we need a plan to tackle to social effects of Brexit just as much as we do the economic ones".
It's not about having a go at people who voted Leave. It's about looking at how we recover from what has been a very divisive campaign about our future as a country.