The woman answered the door to her home in Russell Hill Road, Purley, south London, to find a man outside, police said.
He used his foot to force the door open and barged in to her home. He first assaulted her before raping her.
A 46-year-old man was arrested on Saturday on suspicion of rape and remains in police custody.
A man has been arrested on suspicion of raping a woman in her 70s who was attacked in her own home.