Asim Khan caused the injury as he tried to ram police cars as he was boxed in during the incident in Wakefield.
Leeds Crown Court heard the incident happened at around 11.40am on Monday, March 8 this year on George Street.
Officers were alerted to CCTV images of Khan driving a VW Passat.
Richard Holland, prosecuting, said police had been carrying out an operation at the time to clampdown on drug dealing in Wakefield city centre following complaints from residents.
The Passat was seen pulling up next to two known drug users with one of them getting into the back of the vehicle.
Three unmarked police cars were on the scene within two minutes and parked around the Passat to stop it escaping.
Despite Khan initially lifting his hands to apparently surrender, he then reversed at speed, hitting the officer and trapping him between the Passat and the police car.
As he tried to then go forward, he was tasered by another officer and crashed into railings.
The officer was taken to hospital but released later that day, having suffered a fracture.
He did not require surgery but was off work for around six weeks.
Large quantities of drugs were found in the Passat, including 53 bags of crack cocaine and 26 of heroin, along with £340 in cash in a bag belonging to Khan.
The 24-year-old was arrested and gave a statement during interview, claiming he did not know it was the police.
This was despite them being in uniform and the car parked in front of the Passat having blue flashing lights.
Khan was found guilty of causing serious injury by dangerous driving and possession of class A drugs with intent to supply after a trial
He pleaded guilty to charges of having no licence, insurance or MOT.
His passenger, 20-year-old Jamie Fullalove, pleaded guilty to possession of class A drugs with intent to supply
He has a previous conviction for dealing in Class A drugs, for which he received a suspended sentence.
Robin Frieze, mitigating for Fullalove, said that after being arrested on that previous occasion, he had around £800 of drugs confiscated from him, for which he was told by his drug dealer he would have to pay for.
As a result, he returned to drug dealing to try and pay off the debt.
Mr Frieze said: "It caused him problems but he knows that the responsibility was his and the decisions he made were seriously wrong ones."
He said Fullalove's mother has since had to move house because of the constant threats, and he was forced to leave the family home.
Both defendants are from the Bradford area.
Paul Addison, for Khan, said that it was "not obvious" that the police officer was immediately behind his vehicle when he reversed.
He said: "He wishes to apologise to the police officer for the injury and distress.
"If possible he would like to say his apologies face to face. If that's not possible, he intends to write a letter.
"He studied for a degree, so he is educated, he comes from a respectable family and his mother is a teacher. It's something of a mystery as to why he became involved in these matters.
"He has damaged his own reputation and that of his family."
The Recorder of Leeds, Judge Guy Kearl QC, said: "You both travelled from Bradford to Wakefield to deal drugs.
"You (Khan) knew perfectly well they were police officers because of the uniforms and blue lights.
"You deliberately reversed into the police car."
He jailed Khan for four and a half years and gave him a four-year driving ban.
Fullalove was jailed for four years and one month.