The 32-year-old player replaced Kamal Kamyabi Nia, who was deemed surplus to requirements by the Iran Professional League (IPL) titleholder.
Rigi started his career in Fajr Sepasi Shiraz in 2011 and has also played in Persepolis archrivals Esteghlal and Sepahan.
Persepolis has previously completed the signing of forward Shahab Zahedi.