The Texans added McGloin last week after rookie quarterback Deshaun Watson tore his ACL during practice on Thursday. McGloin was inactive on Sunday, as Tom Savage started in the 20-14 loss to the Indianapolis Colts, with T.J. Yates as Houston's backup.
Watson is scheduled to undergo ACL surgery on Wednesday with Dr. Walter Lowe in Houston, a source told ESPN.
Johnson was the New York Giants' backup quarterback in 2016 but was released in September 2017. He has not played in a game since the 2013 season, and in the two games he did play that year, he did not throw a pass. He played in one game in 2012, and did not throw a pass in that game, either.
During the 2011 season for the Tampa Bay Buccaneers, Johnson was 19-of-36 for 246 yards, with a touchdown and two interceptions in nine games.