This is fairly complicated question so the answer can’t be a simple yes or no. Roughly you can determine someone’s level of intelligence. After a conversation with someone you should be able to put that person in one of three groups – below average, average, above average. But at the same time you can’t do it thoroughly because your judgment of someone’s intellect is constrained by your own. You can judge someone’s knowledge about certain domain expertise if it is compatible with yours, but knowledge should not be mistaken for intelligence, although a lot of people think that people are more intelligent the higher their education is.
Since the intelligence is usually defined as the ability to cope with new situations, the better method would be if you got him interested in a topic new to him, one that you are good at. While talking him about that you could estimate how much he is following you and what kind of question is he asking you. However, Intelligence does not exist separately from the knowledge and all the other characteristics that make one person, so again even this method can’t be precise. The other thing is that more and more scientist talks about different kinds of intelligence, like logical, mathematical, social, verbal, etc.
Though the conversation you may be able to asses someone’s verbal intelligence, but it would be a lot harder to grade his conceptual or social intelligence. If you after reading this, still want to try here are some ideas that might help you.
Explain something to him
Chose a topic that he does not have previous knowledge about, explain it shortly with pauses while talking. When you make pauses try to estimate that person understanding of what you are saying. Does it seem easier or harder for him then for other people you already explained this to? Pay attention on his questions, specifically does he manage to differentiate more and less important stuff. Does he focus on trivial things or does he recognizes crucial parts of the explanation.
Get him to explain something to you
When he explains it note the way he does it. Does he try to take into account your previous knowledge about it? What kind of a vocabulary he is using while he explains? Interrupt him and ask him to explain some connection between what he is talking about and something else. This way you can see his understanding of a topic and how he links things between fields he is good in and others. After you finished your conversation you would be able to conclude few things about his thinking and his intelligence. Of course, you can never predict what kind of day that person had, how interested he was in the conversation, or some other influences that could affect the way he spoke to you.