There are calls for the Scottish Government to intervene in the dispute, which will affect ferries to Orkney and Shetland.
The ballot for industrial action was called by the National Union of Rail, Maritime and Transport Workers (RMT) after the new private operator of the routes, Serco, announced in October that it was seeking to shed 36 posts on the services from Aberdeen and Scrabster in Caithness.
Of the 108 who voted, 95 said they were willing to strike.
The RMT said that despite extensive meetings over possible restructuring, Serco had abandoned any pretence of negotiation.
But Stuart Garrett, managing director of Serco NorthLink Ferries, said: “NorthLink Ferries remain hopeful that dialogue between the employer and the RMT will continue with the objective of avoiding industrial action.”
Orkney’s Liberal Democrat MSP Liam McArthur is demanding that ministers intervene.
He said: “The contract to provide these services was renewed this summer by the government subject to conditions set by ministers. So the terms of the contract are the Scottish Government’s responsibility.”
Serco won the £243 million six-year Northern Isles ferry contract in May.