The company supplies Scotland-London operator London North Eastern Railway (LNER) from Edinburgh.
The move followed unanimous backing for the walkouts among staff voting.
The RMT said 24-hour strikes would start at 6am on July 14, 17-18 and 31.
It claims staff faced disciplinary action after The Scotsman revealed managers had told them to make up symptoms to get Covid tests after an outbreak.
RMT general secretary, Mick Lynch, said: “This dispute is all about respect and justice in the workplace.
"A culture of bullying and harassment has been allowed to develop at Edinburgh Waverley which has led to a wholesale breakdown in industrial relations.
"Our members are saying enough is enough.
“It's now down to Rail Gourmet to tackle these long-running and deep-seated issues and ensure our members are no longer confronted with this toxic working environment.”
A Rail Gourmet spokesperson said: “The wellbeing of our colleagues is paramount to us, and any form of bullying and/or harassment is completely unacceptable.
"Allegations made to this effect are taken extremely seriously and are, without fail, fully investigated by the business.
"We have repeatedly asked the RMT for evidence of their allegations, but have yet to receive a response.
"With this in mind, we’re disappointed a strike has been called, but this will only involve a small number of colleagues, and we are confident there will be no disruption to our service or inconvenience caused to passengers.”