NFL's Joseph Randle: Arrest Video ... 'This Is the End of My Career'

Ex-NFL running back Joseph Randle knew the impact his latest arrest would have on his future -- telling the Irving PD, "This is the end of my career."

TMZ Sports obtained footage from Feb. 1st -- the night Randle was taken into custody in Texas on a speeding warrant. Randle had appeared at his baby mama's house -- but wasn't welcome and cops were called.

When they arrived ... Randle tried to explain why he was there in the first place ... but he makes little sense.

Eventually, cops ran Randle's info and saw the warrant -- and were instructed to take him into custody.

As police put Randle in cuffs, he knew he would be back in the news.

"They're going to put this all over the place ... 'Randle arrested again.'"

Randle has since been released from custody. So far, no word on when he's due back in court.