Aqua regia is excellent for dissolving gold - in fact it's most likely too aggressive for nanorods (typical etch rate 10 microns/min or more). You can try to improve control by diluting the aqua regia with a little water, or (better in my opinion) you can start with a milder etchant, like iodine-potassium iodide. For the simple recipe see:
This etchant etches at ~0.5-1 micron/min. If that's still too fast, you can try to use a lower concentration of the oxidant, i.e. elemental iodine. Or dilute your process solution; apparently you can go down to ~25 nm/min by using 150 ml of water instead of 40 ml (Geissler M., Wolf H., Stutz R., Delamarche E., Grummt U.-W., Michel B. and Bietsch A. 2003 Langmuir 19 6301, as quoted in DOI 10.1149/2.0111501jss).