In a comment to this question, it was said that
Radiocarbon dating won't work. For a start the tree needs to be dead, which since you're not using the rings I'm assuming it isn't. Also the atomic testing in the 20th century completely messed up the level of C14 in the atmosphere, so radiocarbon dating can't be used for anything that didn't die 70 years ago or more.
I did not know this. So, what kind of dating techniques biologists use today? :-)