Yes, it's possible using Apple's iCloud Drive.
With iCloud Drive, you can safely store all your presentations, spreadsheets, PDFs, images and any other kind of document in iCloud — and access them from your iPhone, iPad, iPod touch, Mac or PC.
Following are the steps to upload your favourite pics on iCloud:
Step 1: Open your favourite photo from photos app which you would like to upload on iCloud.
Step 2: After opening it, go to options
Step 3: Select Add to iCloud Drive option
Step 4: Select iCloud drive from the list. If you want to save your photo inside a folder present in the iCloud drive, choose that. For example, here if I want to save the photo in AI T2 folder I can choose that by tapping on it.
Here's the pic after upload:
Make sure you have iCloud Drive app on your iPhone. If you don't have it then go to the App Store and search for iCloud Drive. Since, you are on iOS 10 you can download Apple's builtin apps from App Store (and delete them too). If this doesn't work, Go to Settings -> iCloud -> iCloud Drive -> Switch Show on Home Screen to On.
Here's the iCloud Drive app on the homescreen.