Vonzell Speight, 42, was arrested around noon at a homeless shelter on Liberty Street.
Speight is chared with first-degree sexual offense, second-degree kidnapping, robbery with a dangerous weapon, first-degree burglary, communicating threats and assault with a deadly weapon.
A woman told officers she woke up around 4:40 a.m. Thursday and saw a man in her room.
The man, who was armed with a knife, sexually assaulted her and took her wallet and jewelry.
Investigators believe he entered the victim's apartment through a back door.