No. We should think of our frog enclosures in much the same way as we would think of a fish tank. They are beautiful, but not to be touched.

The simple answer is that holding your frog can cause them stress, even if it doesn't seem to mind. Stress in turn may bring illness or even death. The less simple answer is that the amount of sodium, along with oils found in human skin, are toxic to frogs. As you might remember from when you were a child, after handling a frog for a long period of time, it would go limp when you tried to release it. They usually lived in my experience, but it certainly isn't good for them. On a less common note, sometimes the skin can be torn slighty if your hands are dry. It may not be evident yet, but when the frog suddenly becomes ill, you know the possible culprit.

from Litoria