Q:

Use a wildcard ssl cert to sign other certs

Is it possible to use a wildcard SSL certificate to sign other certificates? 
i.e. I have bought a root signed wildcard certificate for *.example.com
I want to allow a third party to provide a service for me, on thirdparty.example.com. 
Is it possible for me to create a certificate for thirdparty.example.com and sign it using my *.example.com cert?  Or do I have to buy a separate cert for the third party. 
If this is not possible, is it possible to buy a domain-signing-cert?  Just to be clear, I only want to sign certs for .example.com, not a root level (.com) signing cert. 

A:

No, you can't (although it is technically possible, but it won't work).  Because certificate signing certificate must have two extensions with the following values:

Basic Constraints must be set to CA=True and be marked as critical
KeyUsages extension must have a keyCertSign and cRLSign bits enabled. 

is it possible to buy a domain-signing-cert? 

yes, it is possible, but it would be very expensive for you (if you don't plan to issue a large number of certificates).  Because you will have to pay a huge price for this service, buy required hardware (HSM is mandatory), write documentation (CPS at a minumum) and process external audits to verify whether you comply with provider's CPS (certificate practice statement).  Several time ago I wrote an article about root certificate signing: Certification Authority Root Signing. 
HTH

