Combine 1/2 cup water and sugar in a saucepan; bring to a boil. Cook over medium-high heat 2 minutes or until sugar dissolves, stirring constantly. Remove from heat; cool. Stir in juice and rum. Pour mixture into an 11 x 7-inch baking dish; cover and freeze 45 minutes. Stir pineapple mixture with a fork every 45 minutes until completely frozen and slushy (about 4 hours).
Remove pineapple mixture from freezer; scrape mixture with a fork until fluffy.