Is it the same exact serum from Captain America: The First Avenger ?
All traces of that particular serum were destroyed in the 1940s, and Dr Erskine [much like Dr. Reinstien in the comic] was the only person who knew the exact formula. Even in the 1990 low budget Captain America film, that story detail remains the same; the serum's creator Dr.Vascelli, was said to have "kept the details of the formula in her head", so it "died with her" and no new super soldiers could be made. Howeer, in the film The Incredible Hulk , Marvel attempted to tie the plot points together in much the same way the Ultimates Avengers had, with a nod to the 1970s Incredible Hulk TV show:
In both versions of TIH , Dr. Banner [David in TV, Bruce in the film] was seeking to use Gamma Radiation as the key element ot "unlock the hidden strength" factor; the difference was that in the film version, Bruce Banner [played by Edward Norton] used Dr. Erskine's research into Super soldier production as a jumping of point. Now, considering that Howard Stark likely worked with the government to create the "vita ray booth" that stimulated the cell growth and genetic alterations in Steve, it is possible that, while lacking any real knowledge of the chemical forumla, they may have had access to the energy-emitting device, or plans there of. Considering Bruce may have been doing research into how Gamma radiation can enhance human capability, much like how in the TV show, David Banner noted that human physical output seems to increase with sunspot radiation output, he possibly could have supplimented the "gamma chair" for the "vita-ray booth. This is likely why we see the omage to the TV series in TIH movie's opening scene.
This would tie in well to the Ultimates story line where it was stated that the Hulk had been an inadvertant result of previous research into Captain America's super soldier process. However, that would mean Bruce in the MCU had to essentially reverse engineer the process, "creating" a new type of Super Soldier Serum which would work in line with his already existing gamma research. It's possible then tat he was at least a part of creating the serum in that movie, but again, its unlikely that it is the same serum that made Steve. The end results are simply wfar too diverse.
Lastly, keep in mind that whenever they speak of bruce's work in the MCU, they speak mostly to his work in gamma radiation, not in Super soldier Serum creation, though TIH movie does say he was working on "project" of developing enhanced soldiers.