How to make the marshmallow swirl for Chocolate Marshmallow Ice cream from scratch?
I have made marshmallows using Alton Brown's method; it works and is a lot of fun. If you don't form the individual marshmallows, but just swirl it into the ice cream while it's still a sticky mess, that should work for your swirl.

There is even a video in that link.

As ElendilTheTall mentioned in comments, you probably should reduce the amount of gelatin in Alton's recipe, perhaps by a third, to get a good swirl.