Can a WiFi enabled Arduino make a HTTPS request to my Web Server?
It sounds like a better way to do it would be to have a PHP script act as handoff server (maybe protected by originating IP address) to access the HTTPS site and provide the data over a less processor-intensive protocol.

How to get HTTPS on Arduino?

However, another answer suggests that we are working towards a solution to your issue, but it's not quite there yet (~12 seconds to encrypt a packet). 

https://evothings.com/is-it-possible-to-secure-micro-controllers-used-within-iot/