The defender, 27, was a free agent after leaving Leeds at the end of last season and has spent the last three weeks training with the Championship side.
With skipper Jack Hobbs in the treatment room and Liam Rosenior also injured, Bruce sees his son as a welcome addition to City's defensive ranks ahead of the new season.
"When you look at what's going around on the Bosman market, he makes a very good free transfer," he told the club's official website.
"He's 27 and he'll handle this division. He's at the peak of his career and looks in good shape. I'm sure he'll be a decent acquisition.
"It's imperative you have cover in the right areas and Alex can fill in anywhere along the back line."