If I remember correctly, they used to have one (until about 2 years ago?) but it was discontinued, presumably because there was no way to serve ads through it.
Edit: The Google Web Search API (http://code.google.com/apis/websearch/) was only deprecated in November of last year and should still be usable for a while, although the documentation appears to be gone.
They should just offer a search api and and adwords api together. The publisher can get a cut of the adwords revenue, and there should be some sort of checking that search is being served with adwords - just by looking at comparative bandwith from the one ip.
Edit: The Google Web Search API (http://code.google.com/apis/websearch/) was only deprecated in November of last year and should still be usable for a while, although the documentation appears to be gone.