There used to be a mediaeval church on the site, called Sant'Angelo de Micinellis. It was dedicated to St Michael the Archangel, and appears to have been named after a native Roman family. It was a dependency of the parish church of San Lorenzo in Damaso.
In 1523 the site passed to the Società delle Missioni, which rebuilt the defunct church as a private oratory. The society became known as the Confraternita di San Giuliano by the 18th century. Hence the oratory was rededicated, leading to an obvious confusion with the nearby parish church of Santi Celso e Giuliano.
The site was cleared in 1939 to make way for the modern building now there.
The little street running off the Via dei Banchi Nuovi called Vicolo di San Giuliano preserves its memory. The oratory used to be on the western corner, where number 21 is.
The oratory had a simple rectangular plan, with a square apse and two pilasters on either side wall supporting the ceiling vault. There was quite a long passage from the entrance door.