According to the arrest warrant, the child was smoking marijuana in the video.
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Police have arrested and charged 20-year-old Brianna Ashanti Lofton with two counts of felony child abuse, contributing to delinquency and possession of marijuana.
A version of the video that's received 1 million views was posted by a user who urged the mother's arrest.
The 10-second video shows the hand of an adult off-screen holding what appears to be a cigarillo to the child's lips. The child then appears to inhale and puff smoke.
Police said Brianna Ashanti Lofton, 20, was charged with two counts of felony child abuse, contributing to delinquency, and possession of marijuana, and was taken to the Wake County Detention Center.
The baby has been placed with Wake County Child Protective Services.
Raleigh residents and others began posting the video and comments on the Department's Facebook page just after 9:30 a.m. Wednesday.
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"We appreciate the public's help in this matter," said RPD Lieutenant Jason Hodge. "We welcome and encourage any assistance the public is willing to give us at all times."
Lofton is being held on $100,000 bond.
The Associated Press contributed to this report.