In the first RoboCop film, did the general public know that RoboCop was a cyborg? Or did they think he was a robot with a (partially visible) human face?
Strong leaning on yes.
In one of the news reports, the female anchor (played by Leeza Gibbons) introduces him with this:
Who is he? What is he? Where does he come from? He is OCP's newest soldier in their revolutionary crime management program. OCP spokesmen claim the fearless machine has crooks on the run in Old Detroit.
When OCP executive Robert Morton is interviewed on Mediabreak, he says this:
Here at Security Concepts, we're predicting the end of crime in Old Detroit within 40 days. There's a new guy in town. His name is RoboCop.
From these public facing news clips we can read that he is introduced as both a machine and a man. This strongly suggests that the general public then knows, or it's at least intimated, that RoboCop is a cyborg.
After posting this question and reading Eight Days answer, I think he may be right but for a different reason. From the script:
He's a cyborg, you idiot! He recorded every word you said. His memory's admissible as evidence!
This implies that cyborgs were not unusual in the RoboCop world and their memory even has a legal status. In the dystopian world of RoboCop, the public probably didn't care much, as long as crime was reduced.
Update: in this deleted scene, Bob Morton's first two answers to the journalist's1 questions confirm to the watching world that Robocop is indeed a cyborg:
Journalist: "Mr Morton, is this a man or is this a machine?"
Morton: "Well he's technically an integrated cyborg. I'd be reluctant to categorise him as either, to tell you the truth."
Journalist: "And what about his intelligence? What is his intelligence quotient?"
Morton: [Laughs] "That's a funny question. I mean his memory is computer assisted. And we don't refer to computers as particularly intelligent. Fast, effective? Yes. But intelligent, per se? No, I wouldn't think so."
1 A journalist who sounds suspiciously like the director, Paul Verhoeven.