cURL requires CURLOPT_SSL_VERIFYPEER=FALSE

Thanks to Dave Chen's suggestions, I realized I must have misplaced my certificate. The problem is solved by this certificate which is provided by the cURL creator (extracted from Mozilla): https://curl.haxx.se/ca/cacert.pem

So after downloading this cacert.pem file into your project, in PHP you can now do this:

curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, TRUE);
curl_setopt($ch, CURLOPT_CAINFO, "/path/to/cacert.pem");

Alternatively, this can be set globally by adding the following to your php.ini

curl.cainfo=/path/to/cacert.pem

If you are using WampServer, notice this:

You must put the absolute path in CURLOPT_CAINFO, for example:

curl_setopt ($ch, CURLOPT_CAINFO, 'C:\wamp\www\your-project\cacert.pem')

Don't use relative path: curl_setopt ($ch, CURLOPT_CAINFO, 'cacert.pem') because it doesn’t work.