Heat raisins, water and rum to boiling in 1-quart saucepan; reduce heat. Simmer uncovered 20 to 30 minutes or until raisins are plump and liquid has evaporated. Cool raisins 30 minutes.
Heat oven to 375º. Beat sugar and butter in large bowl with electric mixer on medium speed about 3 minutes or until fluffy, or mix with spoon. Beat in egg. Stir in remaining ingredients. Stir in raisins.
Drop dough by rounded tablespoonfuls about 2 inches apart onto ungreased cookie sheet. Bake 9 to 11 minutes or until light brown. Remove from cookie sheet to wire rack.