Details of the online competition will feature in gift packs of the brand’s Anejo Gran Reserva style.
It will be promoted through social media and price deals in Waitrose and selected independents.
Runner-up prizes include bottles of several rums from the Santa Teresa range and limited edition cocktail kits.
Mangrove managing director Nick Gillett described the activity as a “significant initiative” for the brand.
The promotion runs from April 1 to August 31.