It follows a report of a woman being assaulted near the Tesco Extra store in Newport Road at around 8.20am on Sunday.
A man, aged 29, of no fixed address, was arrested nearby and was still in police custody on Sunday evening.
Staffordshire Police is now asking for anyone with information to come forward.
A spokesman for the force said: "Police have arrested a man on suspicion of rape following a report a woman was being assaulted in Stafford town centre early this morning.
"A man, aged 29, of no fixed address, is in custody following the incident near to Tesco in Newport Road, Stafford.
"He was detained in the local area by officers shortly after the report was received. Enquiries are continuing."
Anyone with information is asked to call Staffordshire Police on 101, quoting incident reference number 193 of August 18.