The charges were brought against Henderson before a video appeared on social media of a West Midlands Police officer trying to speak to the 31-year-old about the allegations.
Police said the alleged victim told officers she feared for her safety following a “verbal confrontation” in New Street.
Henderson, of Brook Street, Birmingham, was arrested on July 5 and charged with breaching public order laws.
He appeared at Birmingham Magistrates’ Court on July 6 to answer allegations of using insulting, threatening words or behaviour, and using racially aggravated insulting words or behaviour.
Magistrates bailed Henderson to reappear at the same court on September 6.
Birmingham West & Central Police Superintendent Andy Beard said: “We received a call from a lady walking through central Birmingham making allegations that she had been sworn at and that derogatory comments had been made about her appearance.
“We have investigated those claims and as a result a man has been charged.
“People absolutely have the right in law to freedom of speech and visitors to Birmingham city centre will regularly hear people offering their opinion on a wide range of topics.
“However, people must do so lawfully and if there is any suggestion anyone is abusing that right and using words likely to cause harassment, alarm or distress or cause a breach of the peace then we will investigate and take the appropriate action.”