There is an option on the Android version of Google+ which lets you automatically back up new photos to Google+ privately. To back photos on Google Plus do as follows:
1. Make sure Syncing option is enabled
2. Open Google+ application on your Android device
3. Press Menu Button and then select Settings
4. Tap "Camera & Photos" and then select "Auto-backup"
5. Slide the toggle button on the top right to enable automatic photo back on your Google+ account
6. You may also change some settings: backup photos only when you are connected to a Wi-Fi network, Disable back up process when on Roaming and Enable the backup only while the phone is charging.