Chapman, star of Dog the Bounty Hunter, was heard using the 'n' word six times while he tried to get his son to break up with his girlfriend, but he also said he did not care that she was black during the clip.
The National Enquirer was the first to post the recording on the internet, but it has not confirmed who recorded the conversation and how they got hold of it.
In a statement, Chapman said that he has the "utmost respect and aloha for black people who have suffered so much due to racial discrimination and acts of hatred".
"I did not mean to add yet another slap in the face to an entire race of people who have brought so many gifts to this world. I am ashamed of myself and I pledge to do whatever I can to repair this damage I have caused."
He added: "My sincerest, heartfelt apologies go out to every person I have offended for my regrettable use of very inappropriate language. I am deeply disappointed in myself for speaking out of anger to my son and using such a hateful term in a private phone conversation."
The bounty hunter also claimed that the recording had been taken out of context, saying: "I was disappointed in his choice of a friend, not due to her race, but her character. However, I should have never used that term."