After a recent trial period, the 33-year-old defender has put pen-to-paper on a one-month deal that will run until Friday 26 October.
Blues moved to bolster their ranks with the acquisition of Robinson after recent injuries to the defensive quartet of Stephen Carr, Paul Caddis, Pablo Ibanez and David Murphy.
Lee Clark told bcfc.com: "I'd like to thank the Board for allowing me to bring in Paul, an experienced defender who will enhance our playing squad.
"While I have been impressed with the progress of our young defenders, recent injuries had left us with just two fit senior defenders so the acquisition of Paul was one we needed to make. As a senior professional, Paul will give us that added experience which is always useful in this competitive division."
Robinson, a former England Under-21 international, began his career at his hometown club Watford before moving to West Bromwich Albion in 2003 and spending six years at the Hawthorns. A season-long loan move to Bolton Wanderers was made permanent in 2010. His spell at the Reebok Stadium was briefly interrupted by a month-long loan to Leeds United last season.
The new recruit has been handed first-team squad number 30.