The standards that control the Rockwell hardness scales, I forget what they are, allow for testing on round material, with a multiplier. You could also mount/polish and do micro-hardness. I've heard of a vickers/knoop macro hardness machine, but I've never seen one.
That size (0.125") is probably too small to measure directly by Rockwell. You can measure by preparing a cross-sectional mount and then use a microhardness indenter (Vickers or Knoop). You can then convert hardness to another scale of interest using ASTM E140. The conversion and applied load will be dictated by the material you are testing. Note that certified hardness conversions do not exist for certain material like austenitic stainless steels.
Superficial Rockwell would work fine. Just pick the correct scale. File or grind a flat on the OD for better readings. The curvature corrections are not very good.
For accurate values you should section, mount, polish and do either superficial Rockwell or low load Vickers (or Knoop) or microhardness.
This is big wire, lots of options.
You could pull the rod in tension and measure the load it took to break. Divide that by the cross-sectional area and get the Tensile strength. Look up in one of the ubiquitous hardness to tensile conversion charts floating around and find the hardness in whatever scale suits you.
Hey, I've had a lot of people tell doing the reverse is an acceptable way of determining the tensile strength; so why not?
If using microhardness, do not make the load too low. George Vandervoort recently published an excellent survey showing how low loads can impact the accuracy of measurments. You should be fine though if you use a 500g load.
Regarding redpicker's suggestion to pull a tensile: I generally find much more variability between tensile and measured Rockwell hardness than I do using microhardness techniques. Both conversions are considered estimates but microhardness is more accurate. Also, tensile conversions only apply to steel (you never mentioned the rod material). They are listed in ASTM A370.
I've done a similar test before. I used Vickers Microhardness test and works out well. Use 500g load. Test was done with a Zwick/Roell Indentec ZHV. Link
