I, Susan, swear to blah, blah, blah.
In your example, the title means to stress that a robot has self-awareness and is "a person". The Robot is capable of saying "I, Robot". This is actually the theme of the movie (sorry if I'm spoiling it for you).
The movie is actually based on a collection of stories by Isaac Asimov also titled "I, Robot".
Another famous use of such a title is a novel by Robert Graves, "I, Claudius". This was also a highly regarded BBC serial also called "I, Claudius".
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