Scientists haven't proved that happens - but France is changing the law just in case.
The French government doesn't want to stop kids having mobiles completely, but would prefer they didn't put the handsets to their heads.
Advert ban too
That means using headphones instead.
French children talk about mobiles
The law could also mean a ban on all mobile phone adverts aimed at under 12s.
A spokesperson for the French government said: "To show children using mobile phones on TV for example would be forbidden. It would be forbidden to develop special mobile phones for children under 12 years old."
French pupils Margaux, 11, told Newsround: "I don't use my mobile often, I can live without it."
But Emeric, 12, said he wanted have a choice on how he spent his money: "I think that it won't be fair for me, because it's my money and I can do anything I want with it."