The 30-year-old Hungary international made 18 Premier League appearances for Rangers last season but has been without a club since leaving Loftus Road over the summer.
Pompey boss Michael Appleton told the club's official website: "Akos was playing Premier League football last season, but he's here because he just wants to play football.
"He's a very good player who can play off a striker and pick a pass - he's a fantastic addition to our squad."
Buzsaky could make his debut when Portsmouth travel to Yeovil on Tuesday night.
Pompey can only sign players on one-month deals as they remain in administration.