Try:
1)
- in Xcode make sure you have followed these 3 steps:
a) Add node_modules/react-native-orientation/iOS/RCTOrientation.xcodeproj to your xcode project, usually under the Libraries group

It should show up somewhere in a list like this:
b) add libRCTOrientation.a (from Products under RCTOrientation.xcodeproj) to build target's Linked Frameworks and Libraries list
It should show somewhere in a list like this:

c) Add $(SRCROOT)/../node_modules/react-native-orientation/iOS/RCTOrientation/ to Project Name -> Build Settings -> Header Search Paths
Make sure that path is correct, in my case I had to add /../ inside it, as above for my RN project, the rn-orientation docs specify that without /../.
- in Xcode go to Product menu and run Clean build folder
- run
react-native run-ios
If it still doesn't work try
2) Xcode go to Product menu, Schemes, Edit schemes, Build and make sure parallelized build is NOT enabled in Build Options

If it still doesn't work:
3) try to clean all the caches and restart npm:
rm -rf $TMPDIR/react-* && rm -rf $TMPDIR/metro-* && rm -rf $TMPDIR/haste-* && watchman watch-del-all && rm -rf ios/build && rm -rf node_modules && yarn install && npm start -- --reset-cache
If you don't have yarn installed just replace yarn word with npm in the above command.
Source for Xcode add library steps: https://github.com/yamill/react-native-orientation
UPDATE: RN 0.60+ supports autolinking and after installing the library with yarn or npm, running a pod install in ios folder, a cache clean, a JS server restart and a rebuild should fix such issues.