As we previously reported ... Carton was arrested by FBI agents last week after officials say an investigation revealed he bilked investors out of millions of dollars in an effort to pay off a massive casino debt.

Now with charges looming, Carton has tendered his resignation at WFAN -- which is owned by CBS radio.

Carton says ... "For 10 years I've had the great privilege of showing up to work every day at my dream job. I have nothing but love and respect for my co-host, the show and the entire CBS Radio family and I've always tried to represent them in the best possible light."

He continues ... "Unfortunately, the unfounded legal issues currently plaguing me will only be a distraction to everyone at WFAN and the show I helped build. With that in mind, I have submitted my resignation to the station and they accepted."

"I am sad to see this chapter of my life close but know that it will allow me to focus on my family, my well-being and clearing my name, while giving the show the best opportunity to succeed without further disruption."

Carton says he badly wants to tell his side of the story to his listeners, but "can't at this time."