The 30-year-old was a free agent after leaving German outfit Darmstadt 98 last season, where he only made two appearances.
Obinna has featured for the likes of Inter, West Ham, Chievo, Malaga and Lokomotiv Moskow.
City confirmed the news via their Twitter account on Tuesday evening.
"Cape Town City FC is excited to announce the signing of former @Inter and @WestHamUtd striker Victor Obinna!," City tweeted.
Obinna also boasts experience at international level, having made 46 appearances for Nigeria.