Is there any relationship between sensitivity of rogowski coil and voltage rating of coaxial cable with it. For example if I just have the sensitivity of the coil and spec of coaxial cable, is there a way to calculate current rating of the coil?
The coil as such doesn't have a current rating cause it doesn't care for the current that flows through your wire. The coil just recognizes the dI/dt and produces a corresponding voltage based on the coil's sensitivity. A very high dI/dt can cause high voltage peaks, therefore you need to specify the voltage rating of the coax cable, and even more important, the following integrator needs to be designed accordingly. The actual measuring happens with the integration of the coil's output voltage, for that reason you cannot reliably measure DC (unless you do the integration in software).
A Rogowski produces and voltage corresponding the the current in the centre. This voltage can be thousands of volts, or it can be micro volts, it depends on the coils sensitivity (turns + coil diameter and coupling at the ends), current and the frequency. The voltage rating is defined only by the insulation between turns. Typically in coils anodized wire is used so that is the limitation. There is no relationship between this insulation and the sensitivity. The current rating will depend on the wire thickness. However rogowski coils typically have weak coupling, meaning if you load the coil (trying to draw any significant current) the voltage will begin the collapse thus your measurement will be wrong. So the integrators always use high impedance opamps. Something like a clamp meter with a magnetic core has good enough coupling a capacitor alone can be used as you can load it a little more, but not a rogowski.