Unless someone has already written a wrapper for libcurl that exposes it via COM's IDispatch (and have made sure that the return arguments are in a form that the Microsoft Script Engine can handle) then you are out of luck. Googling doesn't provide any evidence that anyone has done this.

If all you wanted to do was make HTTP and HTTPS calls then an alternative is the MSXMLHTTP object that is part of the MSXML parser. While is is designed for making HTTP calls to fetch XML it can be used just as easily to get the contents of web pages.

Here is a quick example of getting the contents of a webpage.

(warning, untested code...)

Dim oXmlHttp
Dim sWebPage

set oXmlHttp = CreateObject("MSXML2.XMLHTTP")

oXmlHttp.open "GET", "http://www.norman.cx/", false
oXmlHttp.send ""
sWebPage = oXmlHttp.responseText