All 14 of the firm’s 20 Edinburgh-based workers who took in the ballot voted for action, the Rail, Maritime and Transport union (RMT) has announced.
A decision is awaited from the union’s executive over strike action.
The company supplies train firms including Scotland-London east coast main line operator LNER.
The strike vote follows two staff facing disciplinary action after The Scotsman revealed that workers had been told to make up symptoms to ensure they got Covid tests following an outbreak at the firm.
A manager emailed staff telling them when they booked a test to claim they had at least one symptom to ensure they got a test at a time when only close contacts of those who contracted Covid were offered checks as a matter of course.
Rail Gourmet admitted the instruction should not have been issued.
RMT Scottish organiser Mick Hogg said: “The elected health and safety representative and the industrial representative as well as Rail Gourmet employees have all been subjected to bullying and harassment.
"My members are not only angry, they are frustrated that Rail Gourmet support their employees being bullied and harassed.
"If Rail Gourmet cannot stand up for their employees then the RMT will fight for dignity and respect for all.
"If that means taking action as a principled stance, then so be it.”
Rail Gourmet said it was seeking evidence of the allegations.
Its spokesperson said: “The well being 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 members have voted to take action.
"However, if a strike is called, we will do everything possible to ensure there is no disruption to our service or inconvenience caused to passengers.”
LNER said it did not anticipate any strike having an impact on its catering.