Nautilus International said its members will walk out on August 15 in a long-running pay dispute.
Officers have been taking action short of a strike since June.
The union said RFA officers have experienced a real-term pay cut of more than 30% since 2010, with a below-inflation pay rise of 4.5% imposed in November 2023.
Nautilus International director of organising Martyn Gray said “Strike action is always a last resort for us, but there is a palpable strength of feeling among our members at the RFA.
“Over 14 years of cuts and pay restraint, despite the RFA undertaking increasingly complex operations, have taken their toll.
“Our members are overworked, underpaid and undervalued.
“The fact this is the first time RFA officers will take strike action in history is a scathing indictment on the state of the service that is experiencing a recruitment and retention crisis and rock bottom morale across the workforce.
“Despite early engagement with the Ministry of Defence post the general election, we are yet to receive a new and improved pay offer for our members. This is unacceptable and leaves us no option but to escalate from action short of strike to full strike action.
“Our message is simple, to avoid disruption at the RFA who are vital to the UK’s naval capabilities, we need a pay offer that reflects the high rate of inflation and a pathway to pay restoration. We remain committed to working with government to achieve that.”