In a message to its membership, Community’s national officer for steel said it had “voted to demand a better deal” from Tata.
The company warned workers would lose the “enhanced” redundancy package that was on offer if they went ahead with industrial action.
“It should be noted this resounding mandate has been delivered in spite of the company’s bullying and unacceptable threats to slash redundancy payments,” Mr Davies said.
The union said it would consult members on its next steps.
Mr Davies said he was “urging Tata to reconsider their position and get back around the table” in order to avoid “a major industrial dispute”.
Community’s ballot result follows a vote for strike action by Unite.
A third union, GMB, has also run a ballot for industrial action, which closed on Thursday.
