Is 60 beats per minute a normal heart rate for a 63-year-old male?

This depends on several factors, but is usually considered outside the normal accepted range, so perhaps it is worth getting it checked out by a medical doctor. (You may have a condition known as arrythmia, called bradycardia).

It is impossible to say if you have an arrythmia, which is an abnormal heart beat. You may have sinus (normal) rhythm, just a slowed down rate.

An example of something that causes this is a bundle branch block or other types of conduction block.