In the recording Socha can be heard screaming that she will get his family "lifted" out of the UK before launching into a series of insults.
Socha, who wept as she sat in the dock, had originally denied racial assault but changed her plea to guilty on the first day of her trial at Derby Crown Court.
Mr Iqbal, a 52-year-old father of two who has driven taxis for 22 years, told how Socha called him "every name under the sun" during the attack.
He said: "It was terrible. She called me a Paki, a dirty b******, told me to **** off back to my own country and asked what I was doing here because I was Asian."
Socha launched into her tirade against Mr Iqbal after she accused him of going the wrong way when he drove her and a friend home from another house in Derby at 1.15am on October 1.
When the taxi driver told her he knew what he was doing, she "lost it," according to Mr Iqbal.
Socha had been hailed as one of Britain's rising stars following a string of gritty roles.
She was nominated for a Bafta in 2010 for her breakthrough role in The Unloved, a film about a girl growing up in the care system.
She also starred in BBC1's mini- series Five Daughters, the story of the Ipswich murders, before winning the best supporting actress Bafta last year for Misfits.
Mr Iqbal said: "I wasn't aware who she was. To me she was just another passenger. I was shocked when I heard she was a Bafta-winning actress. If you're in the public eye, you have to set an example. The way she behaved was not good. She was racist."
Socha pleaded guilty on the basis she had "finger-prodded" Mr Iqbal rather than punched him. But prosecutor Sarah Allen said he had suffered swelling to the face after the attack.
Judge Hilary Watson said: "She may have to acknowledge she was so intoxicated her recollection is marred. His recollection was not marred. He was driving a vehicle."
The judge added: "It appears to me that you just lost it. You began to use foul and blatant racism. Your conduct on that night was despicable."
Socha - who has previously publicly claimed anyone who calls a person a "chav" is racist - was also told to pay £450 compensation to Mr Iqbal, and £750 costs.
Mark van der Zwart, defending, said: "She sincerely apologises to Mr Iqbal.
"She has done extremely well for herself, to say the least, and her own behaviour will undoubtedly affect that. She hopes her remorse and explanation will allow her to move on."
- Daily Mail