Most Arborists will have a tree core tool that you can screw in to the center and pull out a "core" showing all the growth rings. Then you count them as 1 ring is made for every year of it's age.
Do this at DBH, that means diameter breast height.
All measurements are taken here in the industry.
This will Not kill the tree, and plug the hole with a filling most Gardening stores have.
All historical trees are done this way.
You will also be able to tell accurately the years back that were drought years.