Can I back up my iPhone remotely? It has been stolen and I need some photos for legal reasons. Thanks in advance!

No, you must have physical possession of the phone to back it up.

Did you sync photos to iCloud (which is not the same as backing up to iCloud)? You can check by logging in to https://icloud.com/photos.

You cannot force a backup remotely. If you had the phone set to backup automatically then it will do so when it can connect to the Internet and other criteria.

How to back up your iPhone, iPad, and iPod touch - Apple Support

see the section: "Automatically back up with iCloud Backup

There is no way to force a backup if you do not physically have the phone.

~Lyssa