ASIHTTPRequest just makes an HTTP request. No more, no less. Since REST is also just an HTTP request, you can use ASIHTTPRequest just fine with a calm web service. However, it does not parse the response, so if the answer is JSON, you still have to parse it.
You can also use ASIHTTPRequest for SOAP, but you need to build XML yourself (or use some other library) and parse the XML response yourself. For SOAP, you can use http://sudzc.com/ instead.