Francis was being held at the Palm Beach County, Florida, jail, according to online records. It was not immediately clear if he already had a lawyer.
Boca Raton police spokesman Mark Economou said that Francis never stabbed anyone with the needle, and there was no indication that the syringe actually contained a substance tainted with HIV.
The incident occurred at the weekend in Boca Raton, according to the affidavit. When police responded to the scene, the Uber driver told them he had been robbed by a man who had since fled.
The driver told officers that a passenger he was transporting before the robbery had asked him to stop at a store, so that she could buy something. The Uber driver parked in front of the store and waited; that's when the robber climbed into the vehicle.
Francis "pulled out a syringe" and told the victim to drive or he'd be injected, the affidavit said.
The Uber driver took off, travelling a few blocks until the robber told him to make a U-turn.
Police said Francis, who still had the syringe, told the driver to pull over, and turn over his phone and wallet. He was captured when police searched the area in the aftermath of the incident.
Authorities found a syringe in one of Francis's pockets and a wallet with the victim's driver's license and credit cards in the other, according to the affidavit.
Francis, who denied knowing about the robbery, told investigators he had used narcotics before he was arrested.
Similar threats of HIV injection have been issued during crimes before: During a service station robbery in Kentucky, for example, and at a casino in the Midwest. The Sun Sentinel reports that it's still unclear what was in Francis's syringe.
It will be up to a court to order a test of the syringe to determine what was in it, police spokesman Mark Economou said. The result of the test would be shielded under medical privacy laws, he said.