The 32-year-old Chile international, who has made only seven appearances for the Serie A side this season, renews his links with City manager Roberto Mancini, who he previously played under at Inter Milan.
Mancini said: "Pizarro is a good player. I think he can help us in the next three months because he is a good player. He has good quality."
Pizarro won the treble of league title, Super Cup and Coppa Italia in his one season with Inter in 2005-06 before moving on to Roma, where he has twice won the Coppa Italia.