The Times newspaper uncovered messages sent to former Warwickshire and Leicestershire player Ateeq Javid, in which Rafiq is seen to make disparaging comments about an unnamed Jewish person.
Rafiq, tweeting about those remarks on Thursday, said: “I have gone back to check my account and it is me — I have absolutely no excuses.
“I am ashamed of this exchange and have now deleted it so as not to cause further offence,” the 30-year-old Pakistan-born cricketer added.
“I was 19 at the time and I hope and believe I am a different person today. I am incredibly angry at myself and I apologise to the Jewish community and everyone who is rightly offended by this.”
Rafiq, a Muslim, was widely praised for giving a disturbing account of the racism he suffered while playing for Yorkshire to a parliamentary committee on Tuesday.
The former off-spinner, whose case has led to further revelations at other county clubs, later said he expected the “floodgates” to open in a crisis that threatens to engulf English cricket.