Sinclair, 45, appeared on the FA Cup Final Score programme on BBC on Sunday.
He later tweeted: “Very grateful to be invited back to the bbc sport team today, made mistakes, accepted responsibility and criticism. Apologise for letting myself down. Trying to be a better person.”
In January, he was ditched as a pundit after he was sentenced to 150 hours of community service and given a 20-month driving ban by Blackpool magistrates court.
He was also ordered to pay PC Gareth Evans, who he also asked whether he was being arrested for being black, £500 compensation, as well as court costs of £170.
Sinclair, of Victory Boulevard, Lytham, had pleaded guilty to drink-driving and a racially aggravated public order offence on November 12 last year.
The court heard he was more than twice the legal drink-drive limit.
He had been a regular on Football Focus and Match of the Day since retiring from the game in 2008.