I have a Leopold VX-II 3x9x40 and the variable power ring has become quite difficult to turn. The scope is probably at least 10 years old. I thought about just trying to put some oil on it, but was not sure if that might have any adverse effects on the scope. Any suggestions.

If it was my scope, I'd return it to Leupold and have them free up the ring. Leupold's have a lifetime warranty, so the only cost to you will be shipping and insurance.
I wouldn't use oil on the ring.

Don

Some times you can get some dirt under the ring which can cause the problem. Send the scope back to have them look at it. You are only out the shipping.

Don & Jon are right on the $$. Send it back to Leupold. In the long run, you'll be glad you did.