Yes, children can take iron if they are deemed by their pediatrician to need it. There are iron supplements on the market, such as Renzo’s, that are made just for kids. It may be easier to have liquid or melt in your mouth forms of iron so that you avoid a choking injury and these also tend to be easier for little ones to take.
A note of caution, however, iron can be very toxic to children, and there are many cases of overdoses reported each year. Monitor your child’s intake and make sure that your supplement has child proof tops or protections and is far out of reach of your child at all times. And, as always, make sure to consult with your child's pediatrician before you buy.