It followed a consultative ballot in which more than 60% voted against the OCA's offer to move to a three-week on, three-off pattern.
A new package was to be introduced to offset the impact of the changes.
The union said the vote increases the likelihood of industrial action in the North Sea.
The OCA said it was "extremely disappointed", and believed the offer balanced the needs of workers with the requirements of business.
BBC Scotland revealed in May that oil giant BP was moving its offshore staff to a three-on three-off rota pattern from January.
The company said the move was for the "long-term sustainability of the business".
The current rota is two weeks on and three weeks off.
The offshore rota pattern has been the subject of speculation since the industry began experiencing difficulties due to the oil price downturn.
Unions have raised safety concerns about workers being offshore for longer spells.
Unite members of the Offshore Contractors Association (OCA) have rejected proposals over changes to shift rotas and terms and conditions.