The industrial action is due to a row over getting paid less for working on days off than drivers.
Three quarters of conductors represented by the Rail Maritime and Transport union (RMT) voted to take strike action, which will start at 0.01 hours on Sunday March 28, ending at 23.59 that day.
It will take place every following Sunday ending May 2 – potentially being extended if no deal is reached with the company, according to RMT general secretary Mick Cash.
Additionally, all conductor members of the union have been instructed not to work any days off or undertake any higher grade duties from 0.01 hours on Friday March 26 until further notice.
The move comes after ScotRail and drivers’ union Aslef extended the deal for drivers to be paid extra for working on days off being extended from January to October. The RMT was angered by the move, coming after its members were told they would not be getting a pay rise when drivers are benefiting from the second year of a previously-agreed two-year increase.
Mr Cash, on calling for the strike action, added: “I ask you all to show your support and stand shoulder to shoulder during the days of industrial action. We must ensure we do not allow Scotrail to divide the workforce and demand that the company do what is fair and honour an enhanced rate for rest day working for all grades.”