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.