Police found the woman's car at the man's home in Katlehong on Tuesday, and arrested him, Captain Steady Nawa said.
Police believed the man knew the woman as she was last seen with him.
"The incident occurred on Friday at the woman's house in Fanstone Road. She was asleep in her bed when the man allegedly throttled her and then stole her car.
"She was found by her neighbours with marks around her neck and blood seeping through her mouth. The neighbours then called the police."
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