Preheat oven to 425°F.
Combine currants, hot water and rum extract in small bowl; let stand about one hour to blend flavors.
Beat margarine until soft in large bowl of electric mixer at high speed.
Beat in sugar, then egg, beating until fluffy; stir in flour and currant mixture.
Drop batter by teaspoonfuls, about 1 1/2 inches apart on well greased cookie sheet.
Bake 5 minutes, or until edges are golden.
Remove from cookie sheet with spatula.
Cool on wire cake racks.