Requests made by RCurl do not use your browser. They should use their own RCURL library to create HTTP requests.
Most likely, the website checks the useragent line of the request to see if something is a valid browser. RCURL does not seem to indicate the default useragent line, as your browser does. If you want to impersonate Chrome, go to http://www.whatsmyuseragent.com/ to find out what your current useragent string is. Copy this value into a variable in R, then run
ua <- "<your full user agent here>" getURL("https://www.viralheat.com/api/sentiment/review.json?text=i%20am%20happy&api_key=", ssl.verifypeer=FALSE, .opts=list(useragent=ua))
and this should avoid the browser step in order to at least bring you to the API.
source share