The Babyshambles' frontman, who has a history of drug use, denies the charge.
He was arrested by police investigating the death of heiress Robin Whitehead, who died from a suspected drug overdose last year.
Whitehead was working on a documentary about Doherty and his former band, The Libertines, when she died.
Doherty, 31 years old, has frequently made headlines for his brushes with the law.
Wearing a black coat, waistcoat, trousers and a white shirt, he appeared in the dock Wednesday along with two friends also charged with cocaine possession - charges they deny.
All three have been released on bail after the short hearing and ordered to appear in court on March 29.