According to the docs at https://cloud.google.com/appengine/docs/php/#dynamically_loadable_extensions and https://cloud.google.com/appengine/docs/php/config/php_ini#GAE_directives
Adding this to php.ini should load the curl extension:
extension = "curl.so"
Similarly, adding this too app.yaml should load a curlish extension:
google_app_engine.enable_curl_lite = "1"
However, when trying extension_loaded('curl') via php the results are false. At least in the development server, I have not yet tried in production.
Any ideas?