Researchers collected survey data on 4,584 students in grades 3, 4 and 5 between 2014 and 2016.
They found that overall, 9.5 per cent of children reported being a victim of cyberbullying.
Children who owned cell phones were significantly more likely to report being a victim of cyberbullying, especially in grades 3 and 4, researchers said.
"Parents often cite the benefits of giving their child a cell phone, but our research suggests that giving young children these devices may have unforeseen risks as well," said Elizabeth K Englander, a professor of psychology at Bridgewater State University in the US.
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They noted that cell phone owners in grades three and four were more likely to report being a victim of cyberbullying. Across all three grades, more cell phone owners admitted they have been a cyberbully themselves.
The increased risk of cyberbullying related to phone ownership could be tied to increased opportunity and vulnerability, researchers said.
"At the very least, parents can engage in discussions and education with their child about the responsibilities inherent in owning a mobile device, and the general rules for communicating in the social sphere," Englander said.