Police said that the driver approached the 48-year-old cyclist on Lion Street in Carlisle around 1.45 pm.
The cyclist was allegedly struck and dragged behind the car for around 30 metres, police said.
The 48-year-old man was taken to Royal Perth Hospital, where he later died from his injuries.
Police arrested the 27-year-old man a short time later and charged him with murder.
Police allege the collision was deliberate.
Detective Inspector David Gorton said several other people were in the car at the time of the incident and they had been interviewed by officers.
The other people in the car are believed to be family and friends of the 27-year-old.
Police do not believe that the victim and the alleged driver were known to each other.
The 27-year-old is due to appear in court tomorrow.