Access and file upload to Dropbox (RAW socket)

If your ultimate intention is to use an ESP8266 to make an SSL/TLS connection to a web server (i.e. https://) have a look here:

http://arduino-esp8266.readthedocs.io/en/latest/esp8266wifi/client-secure-examples.html?highlight=client%20secure

http://arduino-esp8266.readthedocs.io/en/latest/esp8266wifi/client-secure-class.html?highlight=client%20secure

and generally google for keywords esp8266 arduino client secure https ssl tls

You'll see the complexity and limitations.