Police launched an investigation after being made aware of a short video clip circulating on social media channels showing a boy performing a Nazi salute outside Giffnock & Newlands Synagogue.
The boy also appeared to have a Hitler-style moustache drawn above his upper lip.
A police spokesman said: “A 16 year-old-boy has been charged and is the subject of a report to the Procurator Fiscal and the Scottish Children’s Reporters Administration in connection with the incident.”
Further enquiries are ongoing.
East Renfrewshire Council has confirmed it is also aware of the video clip.
A council spokesman said: “We take a zero tolerance approach to the misuse of social media, particularly when it is offensive to others.
“We promote an ethos of equity and equality and foster good relationships in all our schools and this matter will be dealt with in line with those policies.”