The woman, known only as Yazmyn, took pictures of her alleged attacker and posted them on Twitter in an effort to notify Transport for London.
She wrote: "Mixed emotions. Scared, vulnerable, angry that no one bothered to help."
Of the alleged attack, she wrote: "Very threatening and [he] was throwing punches at me.
"Tfl need to have more staff on the platform during the early hours of the morning."
British Transport Police (BTP) confirmed it had received a complaint and was investigating.
A BTP spokesman said: "We have received a report of a woman being racially abused by a man at Piccadilly Circus Underground station shortly after 6am on Thursday, 7 April.
"This incident has been reported to us and officers are now making enquiries to establish the full circumstances of the incident."
Steve Griffiths, Chief Operating Officer for London Underground, told the London Evening Standard: “We do not tolerate racist behaviour on our network and will work with the British Transport Police to investigate this incident.
"Our station staff are now out in ticket halls, on gate lines and on platforms to help our customers make their journeys and keep them safe.
"Crime across the Tube network is at an all-time low and we continue to work hard to ensure our customers are able to travel with confidence.”
Anyone with any information is asked to contact British Transport Police on 0800 40 50 40, or text 61016, quoting reference 288 of 07/04/2016.