Apple - How to upload photos to iCloud Photo Library on iPhone without Wi-Fi?

Unfortunately, the answer is no:

When you turn on iCloud Photo Library on your iOS device or Mac, your photos and videos will upload after you connect to the Internet with Wi-Fi and your battery is charged.

https://support.apple.com/kb/HT204264#upload [emphasis mine]

My father has the same issue he lives in a area where he can't get internet. We have a hack option takes two iPhones or a iPad with Cellular what you do is the phone you want to upload photos off you tether to the iPad or iPhone it will think its on a wifi network and start uploading photos. so take a old iPhone put your sim in it and tether it to the phone and then it will work its a hack and is a pain but does work.