There is more than one approach to tackle this problem.
The easy way out is to add android:configChanges="orientation|screenSize" to the relevant Activity in your manifest. By setting this flag you tell Android to not destroy the Activity and that you're going to handle all orientation changes (if any) yourself.
The more modern approach would be to put the WebView inside a Fragment and make it retain its instance, using the setRetainInstance(true) flag. The hosting Activity will still get destroyed on orientation changes, but the Fragment containing the WebView will simply be detached and re-attached, without the need to re-create itself. You can find an example of this feature in the API demos. Keep in mind that the support library offers a pre-Honeycomb compatible implementation of fragments, so don't be fooled by the API level of the 'regular' Fragment class.