Leslie Small, 51, of Milton, Delaware was arrested early Friday morning at a Milton motel.
Police say Small was driving a taxi, and picked up 78-year-old June McCarson on Thursday.
Later in the day, a Meals on Wheels worker discovered McCarson's body in her home.
Troopers found her trailer was unsecured and there were signs of a brief struggle.
The motive for the killing is unknown and the investigation is still ongoing.
Small was charged with first degree murder, possession of a deadly weapon during the commission of a felony and robbery.