The study was published by The Journal of Pediatrics on Monday.
It found that children who had a smartphone by age 12 were at higher risk of depression, obesity and insufficient sleep than those who did not yet have one.
The researchers analyzed data from more than 10,000 children.
While the study shows only an association between age and smartphone impacts, researchers point to previous studies that suggest that young people who have smartphones may spend less time socializing in person, exercising and sleeping.
Dr. Ran Barzilay, who is an adolescent psychiatrist at Children's Hospital of Philadelphia, was the lead author of the study.
He said, "Many experts have urged parents to delay when children receive their first smartphone because of possible harms to adolescent health, but until now there has been little empirical evidence to support that advice."