Is it normal for my 3 year old son to stutter frequently?

Yes: Yes, stuttering at this age is common and a normal part of speech development and not usually a sign of significant troubles. For many kids, it is not persistent but occurs more frequently with excitement, etc... Speech therapy may help, but not usually indicated and more and more is not paid for for this purpose.

Yes: Mild stuttering is normal up to 5 yrs of age. Note if it happens mostly when exited or trying to say "too much too quickly". If severe, it might warrant evaluation before 5 yrs of age.