That's odd! As a fellow iPhone user, the ICCID displays the full sequence in the Settings. If you're unable to view you may view by removing the SIM in which it's displays.
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That's very strange. The whole number should show without doing anything. When you view in landscape in settings the screen is actually smaller since it's a split screen so that has no affect on how much of the number you would see. Have you reset your phone (holding the home and power buttons until the apple appears on the screen)?
If you have your text size cranked up, set it back to Apple's normal setting to see all of the digits. This can be adjusted in the Accessibility Settings.