Yes you can!
Via Dashboard
The best way to add or edit pet photos from a smart phone is to use either BETA dashboard My Pet List to edit an existing pet, or BETA Add Pet to add a new pet with photos.
The BETA dashboard is mobile optimized.
You can drag photos to reorder them.
You can add HEIC format photos via BETA too!
Via Admin Home
For now, you can still use Adopt a Pet's "legacy" admin area to add or edit photos from most smart phones. While the admin area is not mobile optimized, with some zooming in and out, it should work.
Photos can not be reordered on mobile. Add them in the order you want them to appear.
Photos must be JPG, GIF, or PNG format.
Max photo size is 8MB.
"Mobile Uploads" via email
This tool no longer functions. It will still generate a unique email address at https://www.adoptapet.com/shelter/mobile-uploads but it will not add the photos to your mobile uploads gallery. Use the Dashboard instead.