In a small pitcher or mixing bowl with a spout combine the rum, orange juice, pineapple juice, and angostura bitters.
Pour into your popsicle mold of choice and place into the freezer. Let freeze for about an hour or two until slightly solid and then insert the popsicle sticks. Leave in the freezer until frozen solid, for another 4-5 hours or overnight.
If using plastic molds, run some water over them to loosen up enough to remove the pops. If using Dixie cups, just cut the paper away before enjoying.