Arsene Wenger's men earned their last-four berth with a 2-1 win at Manchester United on Monday, and now face a clash with lower-league opposition.
Bradford, who have already seen of Chelsea and Sunderland in this season's competition, were held to a goalless home draw by Reading Saturday.
Liverpool, meanwhile, will face Aston Villa in the semi-finals if they can come through their replay against Blackburn Rovers.
Championship outfit Blackburn kept their Premier League opponents at bay on Sunday to earn a return fixture at Ewood Park, while Villa saw off Midlands rivals West Brom in a 2-0 win.
The semi-finals will be played at Wembley over the weekend of April 18/19.
