I'm a full stack software engineer who knows how to architect and build enterprise scale applications. I don't, however, have an idea for a business or knowledge of how to execute the business side of things.
How can I find early stage startups that are looking for a CTO? There seem to be very few public listings for CTO roles.
Most early stage startups don't need a highly skilled technical CTO. Or rather, they can't usually justify one.
Assuming you really do mean early stage, and you're prepared to work without salary, then you should be networking yourself in the same places that your potential co-founders will be. Startup Weekends, Hackathons, Accelerators, local co-working spaces, etc, as well as talking to people who aren't looking, but might know someone who is.
disclaimer: I'm a facilitator for Startup Weekend.