First import your current photos to your computer for safekeeping, as explained here: http://support.apple.com/kb/HT4083. You will also need to save any other data on your phone that you want to keep that is not contained in the backup you are restoring to or you will lose it as restoring from an iCloud backup requires erasing all content on the phone.
When finished go to Settings>General>Reset and tap Erase All Content and Settings. You will then go through the setup screens as you did when the phone was new. When given the option, choose Restore from iCloud Backup (see image below), and select the backup of your old phone to restore to. Be sure you are connected to wifi and your charger as this will take some time to finish. Of course, there is no guarantee that restoring to this backup again will recover you photos if it failed to do so the first time. I did see a post once from a user that claimed that they were able to recover their photos by having the Photos app open on the phone during the restore process (see post from ezyjules here: https://discussions.apple.com/thread/4076441?start=0&tstart=0).
When done, to get your earlier photos back on your phone put them in a folder on your computer, then select this folder on the Photos tab of your iTunes sync settings and sync your phone. They will be added to the Photo Library album in the Photos App on your phone.
