The thief, who had made his way into the 92-year-old's home at around 3.30pm yesterday, forcibly moved his victim before stealing a small quantity of cash.
The victim suffered a minor injury to his arm and has been left shaken, police said.
“This was a despicable incident involving a vulnerable man, and thankfully he wasn’t more seriously injured," said Det Insp Mark Taylor, of Bradford CID.
“I would always remind residents that they are under no obligation to let people they don’t know into their home, regardless of their occupation.
“We are carrying out extensive enquiries into this incident and we have extra patrols in the area to reassure local residents."
The incident happened at Kipling Court in Greengates.
Anyone with information is asked to call West Yorkshire Police on 101, quoting reference 13180459147, or Crimestoppers on 0800 555 111.