Texas Attorney General Ken Paxton on Thursday joined a group of state attorneys general suing to block T-Mobile US Inc.’s purchase of Sprint Corp., the latest twist in the cellphone carriers’ marathon merger review.

Mr. Paxton, a Republican, joins a group of Democratic officials from 13 states and the District of Columbia who have asked a federal judge to block the deal, bringing the tally of attorneys general who oppose the merger to 15.

The...