Caution. A baby is not capable of maintaing their position on a swing. That being said there are toddler swings that may be able to safetly place you child in with out them escaping. I would try one of the swings for size. Do not let go of the child until you are sure they cannot wiggle free. I would also suggest that if you feel they can fit in the swing, then just do very small pushes while watching.
4-6 months. A baby can safely be put in a baby swing when he or she has good head control. Usually this is the same age that a baby can be put in an exersaucer or high chair: for most babies, this is between 4-6 months. If you think your baby is ready, try it, and start off slow. If he/she maintains good head control, you're all set. If they seem a little unsteady, maybe try again in a week or two.