Leeper is right. Cast iron rod is the best. But cast iron sold in the store is 1/16 to 3/32 oversize. It needs to be machined to about 0.001 - 0.0015" under the scope tube diameter. There needs to be room for the compound between the lapping bar and the rings.
The lapping compound gets lodged in the graphite pockets in the cast iron. Hence the good cutting action.
The most economical and cheapest for a one off, or once a year job, is cold drawn steel shaft.
It is about 0.001" under nominal diameter.
I machined many shallow grooves in mine with the tip of my regular turning insert. Maybe about 2 to 4 thousands deep.
That leaves a space for the lapping compound. Each edge of each grove, lodges compound in place. That helps with cutting. Not quite as fast as cast, but it works.
Drill rod, or polished rod is too smooth, and a too close to nominal diameter. About -0.0005". The compound sticks better to the softer steel of the rings and grinds the harder shaft down.
Aluminum rod or tube, is never perfect round (from a machinist point of view), and most of the time right on size, or a few thou over. But it works, because its soft. I use it, for final lapping of sizing dies for a commercial lead bullet maker.
Brass rod is right on size as well.
If you use it without machining, or sanding down first, the rings will be ever so slightly to big and squash the scope tube a very little before proper clamping is achieved. It's probably the case for most of the guns out there. Including some of mine. It won't hurt anything, but it's not perfect.
The perfect fit would be, when the ring halves just slightly stick to the scope tube. But its seldom the case with production rings. Unless you lap to just about 100% contact surface.
That's why most of the custom gun makers have scope ring reamers as well.