Kim Leadbeater made the call as she visited Scotland to promote next month’s Great Get Together.
The get together, being held from 22-24 June, is a UK-wide event that encourages people to stage a range of activities designed to bring communities closer together.
It was inspired by Mrs Cox’s maiden speech as an MP, which contained the line “we are far more united and have far more in common than that which divides us”.
Hundreds of thousands of people took part in events around the country last year.
Organisers hope the 2018 weekend, on what would have been Mrs Cox’s 44th birthday, will be even bigger.
Ms Leadbeater said: “The Great Get Together can be whatever you want it to be. It’s not prescriptive, we’re not telling people what to do. It’s using it as an opportunity for something positive across that weekend.
“Whether people want to get together and watch the football, or want to do something on a bigger scale – based around food, sport, whatever – we’re encouraging people to sign up online.
“Really, it’s very much about what works for you and your community.”
She went on: “I guess the call to action today is ‘sign up’. Don’t just sit there and think about it, sign up on the website and do something.
“The good thing about this is it doesn’t take loads of effort, it doesn’t take loads of money.
“You might just need a picnic blanket in the park and a bit of bunting, and it’s as simple as that.
“Whether it’s in your workplace or in your school or local community, come together and do something positive.”
Ms Leadbeater said she hoped the weekend of events, which come two years since her sister was murdered as she arrived to host a surgery in her Batley and Spen constituency, can provide an alternative to the “negativity” and division that can feature in society at the moment.
She spoke as the Great Get Together is set to expand in Scotland this year, with more support from the Scottish Government, local councils and political parties.
She met First Minister Nicola Sturgeon and other party leaders in Edinburgh today to discuss the plans.
“It was a really positive meeting with the First Minister,” she said.
“I wanted to thank her personally for getting behind The Great Get Together.”
Ms Leadbeater added: “Scotland has been amazing and I’m so pleased to be here today to thank you for that.
“People are really really supportive and they’ve got a real appetite for this as a country, which is fantastic. I’d like to say thank you to everybody for their support.”
People can sign up to stage a community event at www.greatgettogether.org.