Tom Sizemore tells TMZ ... he was arrested last night because a guy he barely knows stole a car -- and cops followed the trail right back to him.
According to Tom, the car jacker was a friend of a friend -- and when the guy got arrested recently ... he told cops he lived at the address where Tom resides.
As we previously reported, police came a-knockin' soon after -- ran Tom's license and discovered he had an outstanding battery warrant ... so they arrested him.
Tom tells us, the warrant is the result of a clerical error -- claiming someone at the courthouse failed to log his community service hours stemming from the actor's 2009 spousal battery arrest.
There's an explanation for everything ... right?