I would like to install a new electric cooktop. The panel has a dual-pole breaker serving the current electric cooktop but there is NO marking on the breaker to indicate the rating. The new cooktop requires 60A. Is there a way to determine the rating on that circuit currently without hiring an electrician?
I am assuming you mean there is no marking on the handle or front of the breaker (since that is all you see with the electric panel cover still on).
If that is the case, there should be at least a part number on the side of the breaker, which can be looked up online if the rating isn't part of the part number.
But you will have to turn off the power, unscrew the panel cover, and pull out the breaker to see it. Only do this if you are comfortable installing and removing breakers. If you aren't sure you know how to do it safely, call an electrician.