The score for Family Guy is composed by Walter Murphy and Ron Jones.
Currently there is only one soundtrack release of their music from the show, a limited edition physical CD release which focuses on the first 3 seasons of the series (1999-2001), and half of the fourth season (2005). More volumes of score releases are planned, but it depends on many factors, so keep your fingers crossed!
Currently there is no score available digitally; we are hoping to explore that possibility after the physical limited edition run sells out. Stay tuned for more details on that.