How to respond to a possible supervisor asking for a CV I don't have

The professor probably doesn't want to see your CV in order to determine your competence, but to see your previous research experience, to provide some structure for your conversation.

I'm a bit surprised you don't have a CV from your application to grad school, but regardless, it shouldn't take you more than a few hours to make one, and you'll probably need it in future anyway.

If I were the professor I might have a chuckle over this, but wouldn't treat it as something that makes you "look ridiculous". You are new at the game and can admit that, explaining just as you do here.

I would say that "this is the first time I've been asked for one and don't have one ready". But offer to work something up quickly, though it won't be very formal.

I would accept that explanation. Others might not, of course.

But as JHare suggests, you should get busy.

tl;dr– They probably just want some idea of who you are so they know what they're working with. Probably a good idea to give them something, though not necessarily a standard CV.

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Before contacting this potential supervisor, didn't you check out their group's homepage? Browse through some of their papers, check out some of their projects, and just generally get a feeling for what they're all about?

They probably just want to do the same thing to you. This is, they probably just want to get a feel for who you are, where you're at, and stuff like that so they have a feel for who they may be working with.

Seems like a good, constructive request on their part, and probably something to honor. Though not necessarily with a standard CV – some document roughly like a resume or CV might be suitable.

Thoughts:

1. Probably avoid labeling the document "resume" or "CV".
   If you're not confident about the document representing you as a resume or CV, then probably best to avoid labeling it as such. Instead, you might call it "Personal info", "Background & Education", etc..

2. Focus on constructive bases.
   Give the reader something to work with. For example, if your primary assets are from coursework, then probably focus on what coursework you've done. If you have any special skills that might help – e.g. you're good with programming, writing papers, or building things – perhaps mention it. In other words, help the reader understand what you can do so they know how you can participate.

3. Don't sweat weaknesses too much.
   Often weaknesses can be worked-around. For example, if you're great at writing papers, but you have a pathological inability to save a document, then perhaps you could work with someone else who'd hit Save for you.

In short, it's probably best to give them some sort of idea about who you are in something like a traditional resume or CV, even if not exactly in a standard format.