TRE’s CentrePort Station is the closest one to Arlington — that will put you within about a 20 minute Uber ride, or VIA ride from the station to the drop off area at the stadium.
No trains or buses from DART or Trinity Metro go to Arlington. Restaurants and bars near the Cowboys stadium use to have buses that would take you over there, but I don't know if they do that anymore (I'd call around).
Thanks! Your answer is awaiting moderation.