Place ice cream in a microwave safe bowl and microwave for 45-60 seconds, to slightly melt the ice cream (ice cream should still be cold). Stir to smooth out any lumps.
Add ice cream to popsicle molds, dividing equally.
Add root beer to popsicle molds, pouring slowly to minimize fizzing. Remove fizz with a spoon as needed. Repeat until the molds are filled.
Add sticks and place molds in the freezer for about 4-6 hours, until frozen through.
Notes
It's easier to work with root beer that has gone flat. If you have time, allow the root beer to sit on the counter for about an hour before making the popsicles.
If your mold doesn't come with sticks you can use popsicle sticks. Freeze the popsicles for about an hour, then insert the sticks. This will help the sticks stay in place.
The number of popsicles will vary based on your mold size.
To remove popsicles from molds, run warm water over the outside of the mold for 10-15 seconds.
Serve over ice to prevent/slow melting.
If you want to make a large batch or prepare for a party, transfer frozen popsicles to popsicle bags and store in the freezer.