Can you short out a battery by touching it?

It depends on the voltage of the battery. Usually the internal resistance in the human body is way too high to draw any significant current from a traditional battery.

As an example, touching a 5V battery packs positive and negative poles with a finger on each hand would usually draw less than even one microampere, and wouldn't even cause a minor tingle.

It should be noted, however, that under the right circumstances a, high current, 12V battery can potentially be lethal. If you, for example, have an open wound on both hands and touch the poles of said 12V battery, it could easily cause severe burns or even death. This is because the resistance in blood is way less than that of human skin, and one would draw a much more significant current through this path of blood.