Mount a slightly larger tube in a drill, and file it down to size with the drill turning. Lathe is better if you've got one, drill or flex shaft if you don't - anything that can hold and spin it. Just have to be sure your starting ID is smaller than your target OD!
Or make a drawplate. I've heard you can make one from hardwood (such as oak or maple). It won't last as long as a steel one, but it should be good for several uses. Just drill a hole the right size, and file a taper in it on the entry side.
I also recently learned that for short pieces, you can use a vice to push it through a drawplate. You need a spacer on the exit side so the tube can exit, and a rod or dowel to push the last bit through from the entry side.
If you have a rolling mill with grooved (wire) wheels, you might be able to use that to help get a nice round piece.
Does the inside need to be perfectly round, or just the outside? You could combine techniques: start with larger tube, saw it, solder it, get it as round as you can, then true up the outside by filing while it's in a drill or lathe. (Or start with sheet like you're making tubing, get it as close as you can to round and the right size, then true it up in the drill or lathe.) This will give you a good round OD, but the ID will not be perfect.
Hope something works for you!
