Testing the limits of how far Texas can go to keep migrants out of the U.S., Republican Gov. Greg Abbott on Monday signed into law sweeping new powers that allow police to arrest migrants who cross the border illegally and give local judges authority to order them to leave the country. Opponents have called the measure the most dramatic attempt by a state to police immigration since a 2010 Arizona law — denounced by critics as the “Show Me Your Papers” bill — that was largely struck down by the U.S. Supreme Court. Texas’ law is also likely to face...