Rearrange Photos

What kind of iCloud album are you asking about?

If you open your iCloud Photos Library in Photos on a Mac, you can rearrange the photos in the standard albums freely.

Just drag and drop the photos in the album as you want, or ctrl-click the album in the sidebar of photos and use "Sort > Sort by title" or one of the other options. Or use the Sort command in the "view" menu. You cannot sort the photos in the albums, if you are using a web browser to access your photos at www.icloud.com .

The shared albums cannot be sorted by dragging the photos at all. You can only sort them from the sort command in the View menu. And only in the Photos.app on a Mac, iPad, or iPhone, not in the web interface.

Make sure drag and drop feature is correctly set as described in the article Change Mouse & Trackpad preferences for accessibility on Mac - Apple Support

See the screen shots .

After that you can drag and drop photos from left to right or vice - versa in photo album from Mac photo application see the articles What are albums in Photos on Mac? - Apple Support

Organize and find your photos on your Mac - Apple Support