Is it legal for a parent to slap his child in the u.s.?

Yes, should be rare: Physical punishment is a great way to induce fear but not the best means to discipline a child. Most who study this issue feel that verbal control is the best and physical intervention such as slaps, spankings, etc. Should only be restricted to prevent activities which endanger the child - thus only for extreme situations only.

Slapping a child is: reportable as child abuse, especially if it leaves hand-prints or bruises, or the child is slapped on areas of the body other than the buttocks. Physical punishment is ineffective discipline that teaches physical aggression is okay, A fearful, anxious, angry child has high risk of life-long learning, behavioral & emotional disorders. Parenting classes, family & individual therapy are needed STAT.

Yes but: Each culture defines what its usual forms of acceptable parenting include. Within the American culture, you may be carted off to jail for child endangerment if your neighbor reports this kind of "parenting". Less so if you slapped the kids rear end, but you cross the wrong taboo here and you will need a lawyer.